Question about Beyerdynamic DT 770 Pro

Have been using the headphones for gaming for several years. I have already won several CS:GO lans with them. The headphones are great, even without an amplifier. But I still got the "FiiO E10K" DAC a few months ago to see if the sound would improve. The sound + bass improved minimally.
I would recommend buying the headphones without the amplifier for now. You could always buy it later. (like I did.)

I also used gaming headsets before them. But they are always overpriced and the sound + microphone are almost always worse than if you bought both separately.

I bought these (https://www.digitec.ch/de/s1/product/beyerdynamic-dt-990-edition-250-ohm-over-ear-silber-kopfhoerer-headset-3497040) for gaming (especially Dota2) and am absolutely satisfied, even without an amplifier (mainboard: https://www.digitec.ch/de/s1/product/asus-prime-z270-a-lga-1151-intel-z270-atx-mainboard-6067598). I think the sound is great and they are also very comfortable. You have to decide for yourself whether you want them open or closed. Have fun gaming and researching ;)

You could also take a look at these headphones:
Beyerdynamic Custom Game (Over-Ear)

I also have them for gaming and can only recommend them!

For 80 ohms you should buy an amp, of course you can also do without, but the volume may not be sufficient for you. I also agree with the previous speaker, if you are looking for something exclusively for gaming you are very well advised with the HyperX, after all you also need a mic. (Provided of course you play online games where communication is important, such as cs:go, pubg, etc...)

For gaming, I would recommend a headset rather than headphones.
I personally use this headset: HyperX Cloud II Gaming Headset (Over-Ear, Red)
I am very satisfied with it.