Extensive introduction in an incremental paper?
The answer fundamentally depends on who the audience for the result is. 

If you are addressing people familiar with the conjecture, then your introduction makes sense, because it consisely conveys the information they would be looking for. In the rare case that a novice reader comes across your paper, they may be a bit put off, but can still follow your reference to read the introduction there.

If there is a reason why people not familiar with the conjecture should care about your paper, then you should give those people more. In particular, you'll need to tell them why exactly they should care.