Hello! I think these work quite well for gaming. The extra oomph in the lows and the highs brings out regions that make games fun to listen to, and help highlight things like footsteps.
But first, if you’re looking for a cheaper and well-regarded option that has a built-in microphone you can’t go wrong with the HyperX Cloud II. It’s a blatant copy of the DT770 right down to sound signature. It’s not quite as refined-sounding as the originals, and it doesn’t have the replaceable headband pad, but it comes really close and can be had for a cheap price of less than $100.
If you’re okay with running a separate mic, then pretty much any amp down to the popular portable ones is just fine for the DT770. The 80ohm doesn’t 100 percent require an amp but the 250ohm model benefits greatly.
I’ve used my 250ohm model with a SoundblasterX G5 and a Schiit Fulla just fine, and the Fiio E10k is also a popular choice. Look for something that has an output impedance of under 5 ohms and you should be fine. Most amps will easily handle a 250ohm headphone.
Hope that helps!