I can't speak for chess.com, but I do know Microsoft will stop servacing updates on XP, after next month.
play blocked

Sungksoh- Do you see any icons near the address bar when you try to access the play vs computer page?
I'm guessing you're blocked because chess.com's java app is unsigned. You used to be able to acknowledge the security vulnerability every time you ran, but with the recent java update you can no longer simply acknowledge the risk and continue.
Chess.com needs to update their app and *sign* it to protect its users from running unsigned java which could be replaced with malicious software in the event the website gets hacked.
I could play vs computer before, but after chess.com asked me to update java version which I did, I can not play chess now because it is blocked. Should I turn off MS security essential firewall to play? If so, isn't it very risky?Do others have same problem? I have XP operating system.