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.

Well, I would not write in the same style you wrote, but a similar, even if diluted a bit, message:

Conjecture X on flobby heaps is a major question in modern flap theory. Borkington (2014) proved that Conjecture X is true for all flabby shoves of discrete curvature. In the following, we use the terminology from Kal El (2015). The essential idea of this work generalised Kal El (2015): we postulate that flobby heaps are not only flabby on shoves, but also flippy for fine sheaves. The essential difference to prior works (Barkington 1888, Sockington 1999, Kal El, 2015) is that we iteratively construct a Noether pyramid of flobby flabs (Torkington, 2001) in slob space to show flippiness.

Notice that I would recycle the terminology (it still needs to be briefly introduces, but the lengths can be spared), but keep the motivation. You need to say what are you doing, how it is different from what others did, and why does it matter.