I was wondering if including a rent contract that doesn't include a official stamp is okay or not for a UK visa application.
The current UK Visas & Immigration supporting documents guide asks for Confirmation of legal residence, if you are not a national of the country in which you are applying or your right to reside there is not included in your passport.
What you're referring to is sometime found in a visa application checklist:
Documents showing where you live, such as:
Property deed / mortgage statements / tenancy agreements / accountant's letters / land registration documents
In that case, you can include your rental agreement, a fully-executed (signed) original not photocopy, but it should not need an official stamp. However, if it is not in English or Welsh, it would need to be accompanied by a full translation that can be independently verified by the Home Office.