If we have one casino (more or less provably fair) and 1000 players, all of them using a very safe martingale setup, within a limited time span, say, a year, they will drain the casino bankroll dry, even if some of them are set to bust based on their probabilities. In other words, their combined profits will exceed their combined losses, and it can and most certainly will be enough to drive the casino out of business.
It could, but it absolutely isn't certain. If the house edge is 1% then any Martingale setup, including a "very safe" one (or any setup or strategy for that matter), will average at returns of 99% for the player(s) and 1% profit for the casino. It doesn't matter if there is 1 player or 1000, if some of them bust or none of them do, how "safe" their strategy is. Their expected returns will be 99% of their amount bet.
They
could get lucky and drain the casino dry, but they could equally all go bust and give the casino a nice profit.
This is not how the term has been used here.
Regardless of how you use the term, "zero sum game" has a very precise and clear meaning, in which there is no net gain or net loss between all participants. If you mean something else, then you should use a different term.