Same here. Live games are not working, only on Safari that comes with macOS 26.0 Tahoe.
Mac Safari 26.0 conflict with Chess.com

If anyone with the issue knows how to open developer tools and network tab, it would be really helpful if you could send some screenshots showing what happens when you navigate to chess.com/play/online and when you hit start game button 🙏
In a meantime we're trying to reproduce the issue ourselves.

What @gijs_r shared indicates problems with browser establishing websocket connections. To know if you're impacted the same way all you need to do is just go to https://www.chess.com/play/online, wait a bit and if blue banner shows up - that's your client saying it struggles with setting up websocket. In this state there's no point even clicking Start Game - it won't work.

Our staff is testing the same browser, but unfortunately everything works for them. Here are some ideas for the next things we could try here.
To rule out extensions - could you try starting a guest game in incognito mode?
If you're using a VPN - could you try starting a game without VPN?
If you're on a public network (work, school, coworking space, hotel, mall) - could you try starting a game using your phone's mobile network via tethering?
In incognito mode (a new private window) it works.
I did not use a VPN and am not on a public network.

nice! So this could be one of these two things:
- corrupted cache (clearing it, logging out/logging in should help)
- browser extensions (since they're turned off by default in incognito)
Here's the error message I've got. (In my case, clearing cache and disabling extensions didn't help.)
Turning off private relay did the trick for me. System preferences>iCloud>private relay>turn off until tomorrow.
MacOS 26.0 Safari (which comes with Tahoe) makes Chess.com just plain awful.
Live games don't work at all.
I've tried all the public betas, and now the general release.
Google chrome and other browsers work, for now.