it's a product when running on my computer (i.e. the game)
it's a service when running on their computer (i.e. providing the hosting for downloading, multiplayer client-server hosting).
The issue preventing one practically enacting on software is that copyright defaults to preventing you redistributing it, and you need the source code to be able to modify (fully). Thankfully some games are free software/open source when you can act on your ownership.