I don't think there's any way to rationally argue against someone spending money on something they derive direct enjoyment out of, assuming their spending habits don't destructively affect themselves or others. I mean, even if he spend almost all of his excess income on gacha, as long as he pays his bills, eats well, maintains his mental health and hygiene, etc., it's basically fine. Lots of people develop addictions to gacha though, which I think can be defined as an obsession that leads to destructive outcomes, so even if nothing bad is happening right now, you may be teetering on the line, so it's worth keeping an eye out for that.
As for whether it's an investment, yes, it technically is, in the sense that he puts money in and aside from the direct goods he gets in exchange for the money (the gacha rolls), it is true that the money may contribute in some small way to the company expanding, and thus expanding its range of products, which may also come back to benefit him in some small way in the long run. But I'd say that it's got an exceedingly marginal return on investment. He could achieve the same thing more efficiently by simply buying stock in the gacha company and raising its stock price, then he could also actually earn money from it which he could use for buying more gacha in the long term.