It really depends on the game. And also, game developers know that most users don't have deep pockets to buy the best of the best in hardware so they code for decent "game play" on lessor systems, albeit with less detail, fewer objects, a smaller field of play and other tactics.
That said, while the i3-10100 is an excellent processor, more than capable for many tasks like Office work, surfing the net, updating social networks, watching YouTube videos, playing solitaire, most serious gamers are looking for all those enhancements and so would be disappointed with the i3.
Also, much more than just the CPU is involved here. The i3-10100 has integrated graphics so with a suitable motherboard, a separate graphics card is not needed. But would it be suitable for decent gaming? No.
Then there is RAM. Again, depending on the motherboard, with integrated RAM, a large chunk of system RAM will be stolen... err... shared with the graphics solution for graphics processing. Again, that is fine for those basic Office and surfing needs, but gamers would be disappointed. Instead, they would want a decent, quality graphics card that comes with its own RAM, in addition to a decent amount of system RAM (8 min, 16 or more preferred).
Simply streaming takes little horsepower but recording can consume massive amounts of disk space.
Then, of course, you need a quality power supply to feed all that hardware.
If all that seems out of your budget range, then I recommend considering a decent game console for gaming and a decent PC with at least an i5 down the road when the budget allows.
Otherwise, lower your expectations.
