Eliminate code duplication for root path

The desired behavior for both existing games is identical for the root
path: If there's no nickname set in the session, we want to query for
one, otherwise we server the game-specific template.

And in the last few commits, we actually made the implementation
identical for this function in both games.

So in this commit we replace the two copied functions with a single
function at the top-level. Hurrah for deletion of duplicated code!
This means less boilerplate is required for all future games.