what kind of sound signature did you want?
bass light and more treble/mids focused (ideal for gaming advantage)
neutral and fairly flat (can be dull but also is the most tonally accurate)
v-shaped (accented treble and bass for a more fun sound)
bassy (mids and bass focused)
given you still want to game yet like some bassy music i would say neutral or v-shaped would suit you.
hd598 is a great neutral can. bass is about average but not super strong like you will find in some other cans. fairly neutral sounding and a bit slow but good for long listening sessions.
dt770 (closed) and dt990 (open) are v-shaped. dt880 is a bit more neutral shaped than the dt990 with a bit less treble and bass energy and is good for people who like the signature but want something a bit more toned down. dt770 is more bassy than the dt990 but has a smaller soundstage due to being closed (however is still large for closed cans). dt770 comes in 3 flavors 32ohm/80ohm/250ohm. 32 is normally a waste unless you need portable use. 80 is the most bassy. 250 is the most refined. the premium models sound a bit more airy, have different clamp and covers and are way overpriced. the dt990 has a nice soundstage and is very bright while still having deep bass. its one of the few open cans in its price range to have such good bass. its the opposite of the hd598 in that its not slow but detailed although some may find that harsh and fatiguing but it depends on your preferences. the pro 250 is the best deal. the 770 or 990 are some of the nicest v-shaped sounding headphones in the price range.
akg k7xx is newer so i dont know alot about it but i believe it is supposed to be a bit easier to drive and a bit more bassy than some of akgs other offerings. akg generally has cans with very bright treble and they are normally very picky about source and content. a bad amp or poor quality content generally makes them sound horrible although they can certainly sound really good with a quality amp and good material.
audioengine d1 is a decent combo unit but the schiit magni/modi stack will have more output power. the o2+odac is also worth looking at. if you want virtual surround sound you wont get it with an external dac unless you use razers virtual surround sound (though i did hear if you have a soundcard or virtual built into the motherboard even if not connected direct someone got it to work. i cant verify this but a user posted that to me in a response here). otherwise, you could use a soundcard like the xonar dx (for virtual) and just use an amplifier like the magni.