What does the last `点` mean in `玩得开心点`?
点 or 一点 means some or a bit.

Just like we often use 很 (very) before adjectives and 些 (some) before nouns, we often need 点 just to make the sentence grammatical.

If you omit 点 saying 玩得开心, it sounds like a declarative sentence, rather than an imperative one.

Similarly, we say

快点 hurry up
小心点 be careful
慢点 take it easy


点 somehow functions like a sentence final particle like 吧, 了, etc. It is just used in certain types of sentences.