I have one of those too and had many others. If you want a clear upgrade for gaming from those, the Audio Technica adh1000x has a bigger soundstage better imaging, and they're tuned for the female vocal range which is popular for music in Japan. They're great for gaming, but hard to find. Also really easy to drive, even a gaming console controller can power them.
The Grado 325 is better, but only gaming as the bass is lacking. The hd800s is epic but expensive. The hd8xx Drop makes from a liquidator on ebay is good, then remove the top and bottom stickers inside but leave the middle one for tuning closer to the original at a relative bargain. The hd598 is better than the 560, and the Hifiman he560 is better for gaming than the Sundara. The Sundara has a really wide soundstage but it's flat as a pancake so things in front and behind you are just noticable when something is right on top of you.
The dt990 has good detail, maybe check noise floor if your USB ports are noisy, like a Few smart USB card which I use. Pause a song and turn the volume up to check The Hifiman he6se is great for gaming if you have the power, Adorama has them on sale for $399 if you sign up for the newsletter and search from there.