... neither?
I think they are art.
Is art a product? Is it a service?
Is Chess a product? There are chess boards I can buy, but the game itself is a game. It exists outside the confines of a simple manifestation. This is the same as with video games. The rules of the game are interpreted by a computer, so it's not as immediately obvious but what we are playing is just a single implementation of say, Borderlands. The game itself exists not as a single product or service, but as a construct of interaction between our minds and the minds of the gamewright.
Think about a reskin of quake 2. Is it still quake 2? It plays like quake 2, it uses the same rules as quake 2.
If I replace the pieces in chess with stacks of various height checkers, it's still chess.
In this context, a videogame is but one implementation of the rules using one implementation of the assets. The game itself can be emulated, changed, expanded, or faithful. Look at HD remixes. These specific implementations may be products, or you can choose to see them as the products of a service, but the games themselves transcend the medium and exist outside of it.
Consider in the future when doom is no longer covered by copyright. If we use one of the many source forks of the game engine, and use one of the many upgraded sprite sets, it's still DOOM. The rules are the same, it plays the same... the assets have changed.
I see the original intent to draw attention to these sort of self-destructive games that rely so heavily on DRM servers and the like, but I feel it's important to remember that games are not the bits that we buy on a disk, or pay for the right to download. Eventually these games will lapse back into the public domain, and there they will be.
I do think, though, that we should try to ensure that source code and assets be preserved for this hand over. Consider that publishers of books in the US are required to give a full copy of any book that they wish to publish to the library of congress for the express purpose of transference to the public domain, wherein it can be reprinted and reproduced. I believe that we should be fighting for similar measures with games (as well as software in general).
... but, the poll is too limited. :3
So my vote is unrepresented.