The default site does not use Java at all for client side processes. The old site does use Java for the Play vs Computer feature. If you are on the old site, they won't be fixing anything related to that.
Can't Play Against Computer Using Pale Moon Browser...
Interesting... I did see and try the old site while I was trying to figure this out, but it's on the new site that I'm experiencing the problem. I think the old site was the same though. I'll go check... yeah, the old site gives an error that modern browsers don't support Java etc. and to use the new site.
So if it's not Java, I wonder what else could it be? Any idea what the new site uses for Computer matches?
Well, I've at least discovered that PM gets a score of 400 on http://html5test.com/, whereas Firefox gets 474.
One difference is that PM doesn't support WebGL 2... significantly fewer points in the Web Applications category... a few scripting deficiencies...
I guess PM just must not support HTML5 well enough yet for playing vs. Computer here. Oh wells, will have to use Firefox until it does then. Thanks all.

I know this is a very old (by computer science times) thead, but If someone else by chance arrives on this page, I paste the link to the solution I just found today to this problem that nagged me too https://forum.palemoon.org/viewtopic.php?t=31445.

In a nutshell all that's needed is to install an addon called "Modify HTTP Response", here the essential bits of the thread I linked before (where it is described the problem and the string to past into the box of the addon"
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It's due to missing min/max CSS functions. Here's a Modify HTTP Response workaround (adjust the sizes to suit - 550px for the board, 650px for the opponent choice).
[["www.chess.com",["/style\\.client\\.css$/",["max(var(--boardMinWidth), min(var(--boardMaxWidth), var(--boardMaxHeight)))","550px","/(t: )max\\(.*?\\)([;}])/g","$1650px$2"]]]]
I recently started using the Pale Moon browser due to having some problems with Firefox, and while I'm generally finding it good I've noticed I can't play games here against the Computer; it just gives me a blank page. I tried some Live Chess just to see if that made a difference, and that worked fine so it's clearly something specifically related to playing the Computer.
Is it Java-related perhaps? I've been searching and people have said games vs. the Computer use Java and I'm not sure about how Pale Moon differs from Firefox (which PM is based on) in that regard. Strange that it works fine in Firefox but does nothing at all in PM.
I also see just now that the Tactics page does the same thing, and the Openings page displays the chess boards but not the actual pieces...
Anyone have a possible solution to this? I searched and saw a few mentions of Pale Moon on these forums but nothing seemed to address this issue.