I am glad you received the HD650's. The first thing I would recommend is you use the HD650's for a week or more to let your hearing acclimate to them. Our hearing is affected by what we perceive we want or do not want to hear, so let your brain switch off for a while. Then once you are no longer listening to the headphones and are instead listening to the music, switch back to the HD559's. I believe then you will hear the difference, and noticeably.
On to the amps: yes, you will hear a difference when you switch to a tube amp with the HD650's. The tubes will last you through thousands of hours of listening so unless you are leaving the amp on all the time (not recommended) you will be a nice long life out of them (mine are 2+ years old and going strong). If you do need to replace them, tubes can range from inexpensive (Schiit charges peanuts for replacement Valhalla 2 tubes) to mind-blowingly expensive for some rare NOS (new old stock) units that are highly saught after for this or that reason. I am not into tube rolling at all so I cannot comment on the various tubes but there is no doubt that they can change an amps sound signature, sometimes to a very large degree.
I cannot comment on the gaming aspect as while I do game, I am a casual gammer at best and do not go for the popular FPS but rather racing sims. A Ferrari V10 F1 engine sounds fantastic through them though... that much I know.
Again, I would suggest you take your time, do some research and just listen to the music for a while, then go back and forth and you will see the differences.
One final note, I would recommend skipping the O2; it will not be that much different than the STX. Save your cash for a tube amp.\
Good luck and check back in a week or so...