If you ask 5 different academics, you'll get 6 different answers. There are a couple of points to make though. First of all, your question is subtly different than Diamond's own and that has tremendous effects on how someone can answer it. Diamond's idea isn't that "Europeans came to conquer the world", it's that Europeans were inevitably going to conquer it. The actual process by which they physically did it is simple: They would colonize one place, establish local systems to extract resources for the colonizing country, and use those resources. Sometimes they went to internal wars and crises, sometimes they went towards expansionist wars and conflicts.

Secondly, most academics have a much more nuanced view of Diamond's ideas than simply 'false'. Geographic determinism is obviously a partial factor in how cultures evolve. The Inuit were never going to be agriculturalists, to take an extreme example. Many academics take the view that geography constrains, enables, and eliminates certain possibilities, but it isn't a single factor that will always turn out the same way. Two different cultures in similar geography can construct entirely different solutions to the same problems. Skis vs Snowshoes or the Rickshaw vs the Taxi, for instance.

Thirdly, many of the worst criticisms of Diamond, my own included, are his ideas around inevitability. If you took the earth as a simulation and ran it again, you'd get basically the same result. He discounts other ideas about human agency and non-structural forces in his quest to provide a simple, easy-to-understand model. At the same time, none of his assumptions or variables are particularly explanatory beyond vague handwaving about "# of domesticated animals", "mountainous topography", or "tropical collapse belts". It fails to explain local events such as why state-like structures never emerged in the greater Southwest, despite the presence of nearby states, the same domesticated animals as those states, and climatic conditions similar to those of old world Egypt. his theories apparently only apply at certain scales with no mention of why other scales are invalid or what other factors come in!

Fourthly, I don't personally like Diamond's underlying assumption that European domination of the world is somehow 'its natural, inevitable state'. If we look at the actual span of known human history, the period of European domination of the world is maybe 200 years long starting from the mid-18th century at the earliest. At every point in history before that, Europe had not only not dominated the world, but for most of its history been largely on the periphery of "Great Empires". And current trends persisting, it doesn't appear that Europe will be returning to that dominance anytime soon. Why should a single, small, and temporary part of history that by all appearances is an aberration from the truly multi-polar world we have be taken as the "inevitable" result of structural forces? You can extend Diamond's ideas to cover this issue, but at best it feels like a bandaid over fundamental problems in his model.