The type doesn't matter for gaming only. That said...
The air cooler options are limited at 154mm. [The official max is 155mm(76mm vertical gpu), but I err 1mm less to be on the safe side.]
AIO/CLC goes up to 280mm on the side, but not an option with vertical gpu. Ignoring V-gpu, you should have many more options on this route.
If there's anything to go on:
1)Air cooler would be cheaper over time. A fan failure here or there, cheap to replace. Low maintenance. If there is a more serious downside, it requires a crystal ball in regards to later case or system upgrades.
2)AIO/CLC would be more expensive over time. Fan failure, still cheap. Low maintenance. Downside is when the pump fails, or shows symptoms; you can't simply replace them like with fans - need an entirely new cooler right then and there.
With mITX, it's not just the cooler height to worry about. Most mITX boards severely lack real-estate for all the options, so build Up instead of Out. M.2, audio, chipset coolers, vrm coolers are all vertical mounted, not horizontal.
Wasn't such an issue with the square Intel mounts, but with the later series rectangular, it's more pronounced.
I'd go with liquid cooling. There's very, very few options for air cooling that will physically fit on the mobo, never mind inside the case.