It says drink is «trinkajxo». What would «trinko» be?
I believe "trinko" would refer to the action of drinking - someone correct me if I'm wrong?
trinkado would be better
No. It wouldn't. With verbal roots, the -ad- suffix means it's a repeated or prolonged action.
If manĝ.o is meal and manĝ.aĵ.o is food and trink.a.ĵ.o is drink, what is trink.o?
It's the act of drinking.
Isn't it better to say "La akvo" in this case?
No, because that would be talking about specific water. This sentence is just talking about any water. Does that help, or not at all?
Jes, kompreneble. Dankon!
Sorry, I was on mobile when I replied and I couldn't see that you know a lot more Esperanto than me and the question was from long ago. Oh well, other people might have the same question.
Why is it trinkajxo and not trinkajxon?
Because it isn't the object of any action.
A hint that it's not an object: you cannot use passive voice to make it the subject of the sentence.