It is a wrong definition because it is valid only for the fakecels (many of those self-proclaimed incels). When someone is objectively without home and lives under a bridge he's a homeless person and his homlessness is an objective fact not just a mindset. When someone is lacking attractiveness and despite of his many tries he can't find even one woman to agree being his girl-friend, lover, wife or something like this (for example the so-called "friends with benefits") then this person is an incel (with incel mindset or without incel mindset). There are incels with incel mindset and incels without incel mindset (like many of those incels in denial who don't know that they're incels or doubt it). The analogy with the wealth -- there are poor people with poverty mindset and poor people without poverty mindset but all of them are objectively poor (i. e. they're without some significant material possessions and with low incomes or without any income).
The mindset is important, it's a factor that can help you or fail you but it's a subjective thing which isn't equal to the objective state of the inceldom, poverty and many others.