Wonder what's the word for games bought but never played. ;)
It shares the same "Tsun" as Tsundoku in the form of "Tsumi" (積む/積み, stacking up) and means games that keep stacking up and never been played or finished.
I have been thinking of kickstarting a board game where there will be 500 boxes, 499 contain blank stuff, 1 contains the stuff with the printing materials etc. As long as you leave your copy shrink wrapped yours might be the really valuable one.
(99% of these games are being acquired via HumbleBundle...).
But more importantly this phenomenon is more about the imagined instant access to something, than it is about owning things. A gaming subscription service would be just the logical conclusion to this.