It’s unlikely that any supercomputer would have any games simply because they’re all “work” machines, whether for a research lab, corporation, or government agency.
Besides, the way they’re set up, they probably wouldn’t make good gaming rigs. First off, they’re likely highly optimized for tasks other than graphics; customized (and probably Linux- based) OS and all. Second, most games can’t handle multi-core CPUs very well, while most supercomputers are not only multi-core, but multi-CPU… and not always one that uses the same instruction set as Intel and AMD chips that games are written for.
While it’s theoretically possible for them to run emulators to handle games (most likely written for Windows), the overhead would cause a significant performance hit. Also, re-read the first paragraph.
Comparing a high-end gaming rig to a supercomputer is like comparing an F1 racecar to an aircraft carrier. One is fast fun while the other is far more utilitarian, and while technically more powerful, uses that power to alter the world as opposed to merely entertain whoever is at the controls.