Since it is clear that Norma doesn’t leave the house (see propped up on blocks. and Portieres are drawn before all the windows,), this chimpanzee would be her only companion (we can tell during the film that Max really doesn’t function as a companion, only her servant).
So just as her only companion dies, Gillis drops into her life and eventually replaces it, which is both funny and sad..
Also note that she had 3 husbands prior to this, so it certainly seems like she’s been projecting all her insecurities onto a specific individual until she either gets sick of them or drives them away (or they die). Just an interesting observation from a psychological perspective.
Also reminds me of this joke by comedian Jerry Seinfeld: