Board Game Arena

This.

How hard can it be to have a link to the tournament the game is in on the game page? If it's not part of a tournament, then no link.

Simple.

This already exists.

Here is an example:

https://en.boardgamearena.com/#!table?table=25323061

At the top...
This game counts for tournament: K2 - Up to the sky 2 Winter

and it is even a clickable link.

I too find this mildly irritating. What I think the original poster meant is that while you are playing there is not information on which tournament this belongs to.