Recently, whenever I've tried playing "little chess partner," I get

I get that at a few other websites as well.  The thing is kinda ambiguous, which is kinda suspicious, so I haven't hit either run or cancel yet.  I've just tried to close the dialog box, which is hard 'cause another duplicate of the dialog box pops up whenever I hit the "x" icon.  I can close it through task manager though.  A few weeks ago, I downloaded something that had to do with Java Sun whatever, but I haven't used it.  I was thinking this might be a virus.  Any suggestions?

It says what it says. You downloaded a newer java version and the browser is warning you that this program (Little Chess Partner) uses an earlier version of java compared to yours. It is not a virus.

Most popups "say what they say."  The problem is that they don't always do what they say.  I am suspicious because most security warnings have links to more details... and why does this say "run" and not "continue?"  In addition, most security warnings don't force you to use task manager to get rid of them.  And the "run" and "continue" buttons don't look like normal windows buttons, they look more like hyperlinks.  Can you tell me why you don't think it could be malicious?