Cant we just start a normal thread here instead of posting images of other threads? I could barely read it

Capitalism doesn't come about until the early modern period in Europe around around 1602 when the Dutch East India Company was established. Nevertheless capitalism is built upon the presupposition of constant growth and expansion.

I don't see where capitalism came into this at all.

Yes and no. Conquest is certainly a tool that can help run a capitalist state. But same tool can be used by any other type of state with the same goal. We've been raiding the neighboring cave for mammoth meat long before capitalism was invented. The issue here is that a nation can boost its own economy through conquering foreign territory and add conquered resources to their own, and while it bares some resemblance to how a capitalist state is often based around resource extraction and exploitation, I wouldn't say it inherently means that a capitalist state must do so more than any other type of state.

As for your comment around scientific progress, there are pros and cons. Resources can be invested in a research program, but as long as this is left to the free market and free capital, the research will only be funded if there's a reasonable chance (or impression thereof) that the research can yield results that can be used for capital gain. However, a research project would have no problems finding investors if it appears to be worthy of said investment.

Economics is dictated by three aspects. Land, labour and capital. The first two are self explainable but the last is more nebulous. Capital is usually related to production, something that can generate value/wealth/goods. An example is machinery in a factory, tractors for farmers and even money itself as it can be invested in stocks. Land also has the potential to be capital, oil, fertile soil and natural resources.

Back then most economic output depended on land, labour and natural capital, all of which can be attained via imperialism. However in the modern era countries are much less dependent on such metrics. Technology has filled up labour shortages, education increases output of individuals and are much less land intensive. Not to mention today a country can import all of its domestic needs.

This is why Japan, south Korea and Taiwan are NOT dirt poor. They have little land, labour or natural capital, but invested in lots of capital, producing more wealth and eventually becoming developed economies.

TLDR. No, you do not need imperialism to grow a capitalist economy

Economy is what people make of it. This is why so-called economic "structures" fail.