Without spending too much time on the site, the Sennheiser HD598 (599 now?) is a classic gaming headphone. Check MLE's review.
The HD 599 has less of the high mids/treble focus of the HD 598, and more of a fun, moderate U-shaped frequency response that is more well rounded for wider genres of music and media.
I was looking at the hd660 possibly, didn't really see any reviews of that here, I don't think any of the 650 even?, I should add it wont be 100% for gaming but also movies and music
Just on Head-Fi, there are many audiophile veterans that have reviewed the HD 650:
https://www.head-fi.org/showcase/sennheiser-hd-650-headphones.9315/
The HD 660 S was launched just fall last year, and yet there are still several reviews so far (and an official discussion thread) here on Head-Fi:
https://www.head-fi.org/showcase/sennheiser-hd-660-s.22727/
The HD 650 is a classic, released almost 15 years ago and still well-regarded today. In the first post of this thread,
@Mad Lust Envy wrote a review of the HD 650 specifically when he used it for gaming.
The HD 660 S aims to improve on the series, with a new, more agile driver developed from the lessons learned from making the HD 800 and HD 700. It has a more energetic but still well-balanced sound signature compared to the HD 650. Though not as sensitive and easy-to-amplify as the HD 599, the 150 ohm HD 660 S does have half the impedance of the HD 650, sounding great, for example, straight out of an iPad, or plugged into a Sennheiser GSX 1000 external sound processor or dedicated home amplifier like a Sennheiser HDVA 600 or HDV 820.
Another option is our new GSP 500 or GSP 600 headsets. These have broadcast-quality boom microphones built into the headphones, but can be flipped out of the way to mute them and jam out to music or movies. The previous generation of gaming headsets, the GAME ONE and GAME ZERO, have been popular in this forum and throughout the world;
@Mad Lust Envy also reviewed these, this year, in the first post of this thread. As a HiFi and Pro studio brand, Sennheiser also made these headsets great performers for listening to music and movies.
We are proud of all our headphones, you won’t go wrong choosing any of them