So I have a game that I have published, but I wish to delete it entirely.

And if anyone is willing, can someone explain why a game won’t update to the latest version? I had removed all the code from the one game, and replaced it with a fresh update that is browser friendly, but when I play the published version, it’ll play the version I had removed.

So I have a game that I have published, but I wish to delete it entirely.

To delete a game, you'll need to send a message to the site administrator or post in the relevant forum.

Until they get around to it, you could edit the listing and change its accessibility to "Only people I give the link to", so it doesn't show up on the list of games. And for people who already have the link, you could change both the description and the game content to "Sorry, this game is no longer available" or similar.

And if anyone is willing, can someone explain why a game won’t update to the latest version?

Game files are accessed through a cache to reduce load on the server. If the game has been accessed earlier in the day, the cache will already have a copy and will keep on giving out that copy until it next checks for a new version. This usually takes a couple of hours.