This language is gunna sound abstracted, so apologies in advance. Incels treat human relationships as, to a large degree, calculable and transactional. Attractiveness can be quantified (women can be rated on a scale of 1 to 10). Time and money invested has an expected output. Women seek a positive return on investment with a potential romantic or sexual partner. An incel's goal is to reach that 'minimum rung' and when they find out that relationships also have an emotional component it doesn't fit into their calculus and their reaction to rejection is violent and abhorrent. They accuse women of not following the rules or playing the game properly. I would argue that men who subscribe to the above and still occasionally or regularly have sexual encounters are still incels. It's capitalist realism applied to human relationships.

Edit (I do think this is just one element of inceldom though and doesn't cover other aspects of white supremacy/patriarch etc. so I think my summary is reductive, but as for how PUA/online inceldom instrumentalises and proslytises itself is this 'man does x woman must do y' equations'. The ideology behind it is a black box that ties in the rest of the whole shit show)