Are floor joists allowed by code to be notched at the ends?
The stress on a joist reduces substantially near the ends. For this reason it's often the case that engineered joists have a narrower (shorter) bearing point. Take top-hang truss-joists, for example: 



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Another example is the typical rafter truss. Obviously those are very small at the ends. 

Whether your situation meets any sort of code is somewhat irrelevant. It's a 1940s home, after all. The bigger question is whether it works, and apparently it does. The joist is larger than the others probably because it has a wider spacing due to the chimney, or because it carries some additional load. 

If you're concerned about passing inspection, have a conversation with your inspector. (S)he will specify whether replacing like-with-like is adequate, or whether you'll be required to get an engineer to sign off on a modern approach.