Is it okay to play video games at work?

Depends on where you work. Generally, it's a little weird, but mostly because you're not socializing with co-workers. Otherwise, as long as you're playing with it muted or through headphones, it's not much worse than spending your whole break on your phone. I worked at a game studio for a bit and lunchtime multiplayer was pretty common, no one would have batted an eye. If you work at an accounting firm, it's a little weirder.

When I was starting out, working in tech support before that was completely outsourced, I'd bring my GBC or GBA to work and play on slow nights. Those are the only fond memories I have of those jobs, they were brutal otherwise.