Adding these meta tags to your <head> container should work.
You could also ensure that the URI to your game is always unique upon making changes. For example you could store your main game page on sweet_game.html and use an .htaccess file (assuming you're using Apache server) to access it:
RewriteRule ^SweetGame/?$ /path/to/sweet_game.html
(more on .htaccess rewrites here)
Then, if you ever update the game you can rename sweet_game.html to sweet_game_1.html, and update your .htaccess file to accommodate. And just continuously increment the integer in the filename for each update made.
This would only need to be done for production pages, as you can just manually disable caching on your browser for your development pages (at least you should have both a production environment and a development environment).
That way your users will always have the same URI, which gets redirected (silently, behind the scenes; they won't notice) to the most up-to-date version of the game.
There's probably more ways to do it, but those two are the only ways I can think of right now.