Depends what you're playing saying i3s are not the right tool for gaming is like saying Ryzan 3s are not the right tool for gaming
A i3-10300 is going to be perfectly capable of playing most titles especially at higher resolutions and is $100 cheaper than a 10600k.
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You explained with an article from 2009 that proves your initial post that motherboards have graphics today is wrong.
An iGPU doesn't borrow memory from your motherboard. Your mother board has like 128mb of memory at most, probably 32 or 64. That's not enough to do anything
Modern APUs borrow system memory from your RAM to act as VRAM. Also saying that APUs can't game is really dumb since all modern consoles run an APU.