'Que' serves the same purpose as 'that' in English, in the sense of saying something like "I don't like the fact THAT you ate my cheese" or "It's the one THAT I want". In English, the 'that' can be omitted colloquially:
"I don't like the fact you ate my cheese" or "It's the one I want".
However, in French, 'que' cannot be omitted. This sentence is literally "I want that you eat cheese".
Personally, while I aggree that he changed the tense, I think that in this one case "would like" should be accetped for "vouloir", since it is a 'more accurate' translationof the sentiment, for lack of a better term. To say "I want you to eat some cheese" is closer to the imperative mood, at least in British-English.
Anyway, whatever about "would like", "I wish that you would eat some cheese" should definitely be accepted as a translation of "vouloir".
You can use an infinitive clause if the subject of the two verbs is the same:
- je veux manger du fromage (I want and I eat)
Otherwise, you have to use a subordinate clause with a conjugated verb:
- je veux que tu manges du fromage (I want and you eat)
PS: - "je veux te manger" = I want to eat you