The title is grammatically incorrect. People is already plural, and doesn't require s to make "peoples". The correct saying is "I'm so sick of some people's grammar."
Though I will say that is most likely a mistake, as with other grammar mistakes. Purposely misspelled letters like "ikr" and "bby" are used for shortcuts when chatting at people, which, to be honest, we all used sometimes and can get annoying when overused. Purposeful grammar issues is that own person's fault, but that just leads to the phrase "He isn't that really good at English to begin with."
This is the internet. People will have grammar issues.