What kinds of games are CPU intensive?

Not many. Only really big games and games without dedicated engines such as minecraft. An i3 will still be fine for minecraft

MMORPGs like World of Warcraft tend to be CPU heavy because of having to render large amounts of players and things going on at once. Same goes for RTS games like StarCraft or Total War because you can have hundreds of units at a time.

An i3 might suffice if you don't play on super high settings, but you'll probably want an i5 or better if you plan on playing those kinds of games.

Most current games are much more GPU bound. However with DX12 games will really hammer even the most high end CPUs. I wouldn't get an i3 for gaming, minimum you should be getting is a higher end i5.