In September, Apple changed the iCloud+ plans in 100 or so countries so that an iCloud+ subscription now also gets you access to Apple Arcade, and the non-third-party-branded parts of Apple TV, at no extra cost.
Maybe the invite was to play some Apple Arcade game, a game that requires all participants to be subscribers? And you're in one of the countries where subscribing to iCloud+ is now the way that you would get Apple Arcade? Might explain why opening an invite to a game took you to a page about iCloud+ …
Just a guess ...
(As far as I can tell, the U.S., Canada, Great Britain, Japan, and many Western European countries in the EU are not getting the expanded iCloud+ service. In those places, Apple Arcade would be available via a subscription to it, or via a subscription to Apple One.)