If you are on a public wifi hotspot it could be they are doing some kind of proxying. The cert looks good on my end.
Chess.com certificate invalid

Though, it looks like the cert is registered to a CDN and not directly to chess.com. So maybe that is why it is getting flagged for you.

It's common to import the certificate chain incorrectly which causes Android to complain about otherwise valid certificates. However, I just checked from my tablet and it appears to be fine.
That looks like a much older version of Android, so it's possible it doesn't trust one of the CAs in the chain. You should be able to click on the details and look at the certificate to see what the issue is.

Various chess.com domains appear in the Subject Alternative Name field. This certificate is also shared with ashleymadison.com. Maybe chess.com IS a dating site after all.

Various chess.com domains appear in the Subject Alternative Name field.
I didn't dig that deeply into the cert

My phone is not using an old version of Android. It's 6.0 or "Marshmallow", which I believe is the most current.

7 Nougat is the most current. That said, I don't get the message on 6.0.1 with the default device browser or Chrome (which probably needs updated)

I just got a new phone running Android 7.1 and I still get the warning when using the wifi at my mechanic's shop.
I got a warning about an invalid chess.com certificate when using a wifi.