de rest of it. Den yuhbelong and dey don’t. Den yuh kin laugh at 'em, see? Yuh're de champ of de woild. But me -- I ain't got no past to tink in, nor nothin' dat's coming', on'y what's now -- and dat don't belong.
(Quotes: O'Neill, The Hairy Ape, eoneill.com)

Yank's final realization is that he has had nothing to look back on, and nothing to bring forth as a position of superiority; the gorilla can "dream in the past" and remember belonging in its own world, but Yank can't even remember his own belonging because he has changed and messed it up so badly. He used to belong in the engine room, but being scorned by Mildred and failing to adapt in the city has taught him that his life was small and petty, and he had nothing to offer except his strength -- and that can be had from any number of men. His "belonging" is little more than an illusion in his own head, created to cover his insecurities.

One thing we can notice right away about Yank's attempts to belong is that they are all rather violent approaches, showing us that belonging for him is not merely about fitting in with the crowd but rather about standing out and drawing a great deal of attention.

We see his first violent attempt at belonging when he sees the monkey fur coat on display in a shop window on Fifth Avenue in New York. Not only does he notice the coat, which he likens to himself due to the fact that Mildred likens Yank to a big hairy ape, he also notices the crowd only paying attention to the coat and not to Yank. In his mind, since he and the coat are the same, he should be getting just as much attention. His response is to act in the same manner he envisions an ape would act by trying to pull up a lamppost so that he could batter the crowd with it like a club. His deeper purpose in trying to batter the crowd with a lamppost is not so much fitting in as it is standing out. He wants all eyes on him and, what's more, he wants to be the authority figure.

Yank further shows his desire to be the soul authority figure when he decides to become involved in the Industrial Workers of the World (IWW), an industrial labor organization, otherwise called the Wobblies, who fought for an abolishment of wage labor and the mergence of all laborers into one social class, much like Marx pushed for. He makes the decision because he believes the group uses violence to achieve its purposes. However, it's not simply enough for him to join in on their violence; he wants to be recognized as top dog, the most violent among the group. We especially see his desire to be the most violent and therefore the most authoritative member of the group when in answer to the secretary of the IWW's query if Yank intends to assassinate Mildred's father, Douglass, President of the Steel Trust, Yank's response is to say that he alone wants to blow up the whole steel works factory and all pf the steel in all the world, as we see in his lines:

Naw, [assassination] don't get yuh nothin'. I mean blow up de factory, de woiks, where he makes de steel. Dat's what I'm after--to blow up de steel, knock all de steel in de woild up to de moon. Dat'll fix tings! ... I'll do it by my lonesome! I'll show yuh!

Hence, since all of his attempts to belong are actually violent ways to gain sole attention, we see that Yank's idea of belonging is actually to become the one who is solely noticed and the top authority figure.