If the game starts, but immediately crashes, the final step or process of opening the page on their web site would proceed normally -- it knows the game ran & was shut down, but it doesn't know that you didn't shut it down normally when you were done playing.
WR usually recommends Event Viewer -- I'm not optimistic it'll help in this case, but a quick look couldn't hurt.
howtogeek[.]com/123646/htg-explains-what-the-windows-event-viewer-is-and-how-you-can-use-it/
Microsoft recommends performing a clean boot, which is basically turning off everything that can be turned off for diagnosis -- if something is interfering with the game running properly, then it should run OK if/when you turn that something off. Note that Microsoft hasn't updated their web page to include Win11, but other sites show the process is the same.
support.microsoft[.]com/en-us/topic/how-to-perform-a-clean-boot-in-windows-da2f9573-6eec-00ad-2f8a-a97a1807f3dd
windowscentral[.]com/how-clean-boot-windows-10
Finally, if nothing else has helped, an app called Process Monitor will show you just what happened when you started the game. CAUTION -- using Process Monitor can have very negative effects on your mood, if not your overall mental health [unless you're a masochist]. In a nutshell you start recording, start the game, then stop recording the instant the web page opens. You'll then have probably thousands of lines detailing everything, every read & write to the registry etc. -- there are filters to cut down on the number of lines you're shown, but it's hard to make good use of them if you're unsure what to look for. Search for the game, then start going over every line for some time before that, & continue until you either spot something or are sure you're no longer seeing anything related to the game. Then, if you haven't found any problems, search again from that point, since you may find the game listed again later on. And repeat... [I've used Process Monitor a few times to fix software problems, & while I was lucky enough to be successful each time, it took a few days to get over the effects of scanning line after maddening line, which is why I normally don't recommend it.]
docs.microsoft[.]com/en-us/sysinternals/downloads/procmon