Alpha is the degree to which an investment outperforms "the market", where "the market" can be any benchmark you want to use. So yes, by definition, alpha is zero-sum in that not everyone can beat the benchmark, in the same way that not everyone can be above average.
But this tautology isn't particularly meaningful, because most people don't care about beating "the market"; they care about their financial health and solvency, and in many cases, slightly under-performing "the market" can still be perfectly acceptable for a lot of investors if the market is performing well enough and they've met their own expected targets.
(This is, in fact, the principle behind index funds: index funds will never beat the market, and are guaranteed to underperform the market after fees are taken into account, but yet many people still put their money in index funds).
Alpha is the degree to which an investment outperforms "the market", where "the market" can be any benchmark you want to use. So yes, by definition, alpha is zero-sum in that not everyone can beat the benchmark, in the same way that not everyone can be above average.
But this tautology isn't particularly meaningful, because most people don't care about beating "the market"; they care about their financial health and solvency, and in many cases, slightly under-performing "the market" can still be perfectly acceptable for a lot of investors if the market is performing well enough and they've met their own expected targets.
(This is, in fact, the principle behind index funds: index funds will never beat the market, and are guaranteed to underperform the market after fees are taken into account, but yet many people still put their money in index funds).