As for whether or not capitalism is colonialism and imperialism. I don't know. The connection leftists like to make is that capitalism has markets and property rights as did countries that were colonial and imperialistic. Therefore, capitalism caused the deaths of millions.

No. The connection that leftist like to make is that capitalist relations of production provide governments and private institutions with the impetus to pursue imperialistic goals. Or, in your own words, the argument is that capitalist institutions are extractive institutions and benefit from establishing ultra-extractive institutions abroad.

"Capitalism" isn't just a matter of "markets and property rights" - these existed in a million of societies in an enormous myriad of different forms. Feudal Europe had markets and property rights, the Roman Empire had markets and property rights and even rich merchant capitalists, but it lacked a capitalist mode of production. Capitalism is, in the words of historian Ellen Meiksins Woods:

Capitalism is a system in which goods and services, down to the most basic necessities of life, are produced for profitable exchange, where even human labour-power is a commodity for sale in the market, and where all economic actors are dependent on the market. This is true not only of workers, who must sell their labour-power for a wage, but also of capitalists, who depend on the market to buy their input, including labour-power, and to sell their output for profit. Capitalism differs from other social forms because producers depend on the market for access to the means of production (unlike, for instance, peasants, who remain in direct, non-market possession of land); while appropriation cannot rely on ‘extra-economic’ powers of appropriation by means of direct coercion - such as the military, political, and judicial powers that enable feudal lords to extract surplus labour from peasants - but must depend on the purely ‘economic’ mechanism of the market. This distinct system of market dependence means that the requirements of competition and profit-maximization are the fundamental rules of life. Because of those rules, capitalism is a system uniquely driven to improve the productivity of labour by technical means. Above all, it is a system in which the bulk of society’s work is done by propertyless laborers who are obliged to sell their labour-power in exchange for a wage in order to gain access to the means of life and of labour itself. In the process of supplying the needs and wants of society, workers are at the same time and inseparably creating profits for those who buy their labour-power. In fact, the production of goods and services is subordinate to the production of capital and capitalist profit. The basic objective of the capitalist system, in other words, is the production and self-expansion of capital.

This is a very specific form of market economy that relies on a very specific sort of property rights (the completely ahistorical way in which you mention abstract, ill-defined "property rights" and their relationship to "incentive to produce" is literally unanswerable - it's not even wrong). It didn't arise out of the blue because people found it would be cool to truck and barter.

The claim is that this type of economy, by relying on the extraction of surplus-value and control of means of production by the capitalist class, produces the impetus for capitalists (and the governments they control) to attack other countries with the intention of obtaining key resources and cheap labor. The reason why the British Empire established so many extractive institutions in Ireland and India and China and other places was both because this introduced those colonies into the world market (i.e integrated them into international capitalism) and produced massive profits for capitalists which now had access to cheap resources (taken with guns) and cheap labor (oppressed with more guns) and could thus more easily compete against the French and Spanish capitalists.

As much as i despise the writer, Lenin's Imperialism: The Highest Stage of Capitalism was actually a really good analysis of that for the time it was written (and was a massive influence on Wallersteins World-Systems Theory, which isn't a theory you can simply dismiss). And indeed, the neo-colonial ideologues - many of which were in the 'liberal' intellectual tradition of Bentham and Mill you yourself are influenced by - who supported imperialist ventures used arguments about the need to introduce countries to the world market, benefit private enterprise and "modernize" and "industrialize" countries as excuses for these imperialist ventures, all of those obviously main economic and financial preoccupations of capitalists.

And indeed, many historians historians - Ellen Meiksins Woods, E.P. Thompson, Hobsbawm - have written a lot on the historical ties between capitalism and imperialism, discussing how capitalist development in Europe was largely financed by the extractive institutions they established everywhere else. Just like you shout about the historical connection beween 20th century Communism and dictatorship, there is a strong historical connection between growing international trade based in profit-seeking firms and massive fucking imperialism; even if this latter movement lacked an official manifesto. I recommend Hobsbawm's The Age of Empire: 1875–1914 if you want to read into that.

I would argue the horrors committed by Stalin and Mao were committed for the same reason that European countries during the Golden Age of laissez-faire Liberalism committed the same horrors: The economic and political impetus generated by class relationships. As i stated up there: "The socialist reply that capitalist relations of production did provide certain states and private institutions with the economic and political impetus to cause these horrors (Leopold II of Belgium did treat the Congo as his private property in search of profit, after all) much like economic and political conditions provided these allegedly "socialist" countries with the impetus to commit horrors (Stalin's Russia did forcefully collectivize agriculture in Ukraine with the intention of exporting to finance quick industrialization, after all)".

We know what caused those institutions in the USSR (Marxian thought)

But do we? You haven't established any necessary causal relationship, and as /u/MyShitsFuckedDown3 already pointed out you don't seem to know much about the intra-Marxist debates on what institutions socialism should have.

The blanket statement that "Marxian thought" led to extractive institutions in the USSR is just flat out wrong. First of all, me and /u/MyShitsFuckedDown3 already wrote a lot about how you are dismissing incredibly important sectors of Marxist thinkers that opposed those extractive institutions (including Marx's original work and the most important Marxist theoretician of the 2nd International) and ignoring the fact that Marx's influence is infinitely broader than just 20th century Communism (as i already stated, the vast majority of people who were and are influenced by Marx to a significant degree are not even socialists at all, unless you count nearly all historians and sociologists and anthropologists and world-systems theorists in the world as godless commies).

Second of all, your claim about historical causality is based on idealistic great-man-ism that dismisses the importance of historical, political and economic conditions. I mean, the fact that the USSR literally had 14 international super-powers declare war on it the moment it formed did in fact contribute to the fact a paranoid caste of bureaucrats became it's leadership. The fact it was a semi-feudal country that was still based on exploitative class relationships and that had an imperative need to undergo industrialization did provide the impetus to proletarianize and extract the shit out of the peasantry (much like the British empire did two and a half centuries earlier...).

Like besttrousers already pointed out, the reason why Sudan went from colony to "communist" dictatorship to islamism with little change in it's authoritarian institutions was because the extractive institutions used these ideologies to legitimize themselves. The case that the anti-USSR Marxists have always made was that it was a brutal class society that formed due to historical conditions and which reified "Marxism" into it's official ideology by completely removing the critical and revolutionary content that was at it's core. The reason why this reified version of "Marxism" became the most well-known was because it had a literal dictatorial superpower propping it up and murdering the Marxist opposition (obligatory reference to ice axes and etc), while the other superpower that posed itself as an opponent to it only had an incentive to publicly engage with this reified "Marxism". This is an argument which your line of thinking is literally unable to engage at all, since you seem to take your historical narrative for granted.