Most newer motherboards will run a 600Ω headphone but they won't do it very loudly. You should consider an Amp or DAC/AMP combo for those. As far as an AMP goes what is your price range? It's best to stay under 80Ω on a PC onboard DAC/AMP.
Beyerdynamic 880's are not the greatest choice for gaming, they are an ambient noise vacuum with a mostly neutral sound, they are unstable and mover around on your head easily. They lack any sort of decent bass which means you lose out on a good amount of immersion and certain treble ranges can be quite bright. For example, the Air Raid Sirens in Battlefield 1 are particularly annoying.
I see Monitors suggested often for gaming here but I have to disagree, most all of them just don't have the range or emphasis to really bring out the effects the creators wanted you to hear.