Yes CAP - I agree with you, although I'm not so sure about the distance needing to be an ocean!
Isn't it about a previously agreed distance between two specific points (there and back) - and advertised as such?
Maybe we could also add that a ship (belonging to a shipping line), becomes a Liner when it has been built with the ability and capacity to reach across an agreed distance within in a specific, previously agreed time. In this case it's the Atlantic Ocean - As you mention, it could also be other oceans - for example, the Union Castle Line ships and other Lines also ran Liners across other Seas didn't they?!
There's much more about the definition of the term 'liner' here, via the search engine!
https://www.theqe2story.com/forum/index.php/topic,430.msg21325.html#msg21325To keep to the Topic - interesting to note that the Officers and Crew etc all refer to QV as This Liner! - This Beautiful Liner in fact! It was very difficult not to say something, as she does cross the Atlantic....however, a challenge at the time would have seemed a bit impudent!