They report 2 degradations: code generation & math problems. In both cases, they report a behavior change (likely fine tuning) rather than a capability decrease (possibly intentional degradation). The paper confuses these a bit: they mostly say behavior, including in the title, but the intro says capability in a couple of places.
Code generation: the change they report is that the newer GPT-4 adds non-code text to its output. They don't evaluate the correctness of the code. They merely check if the code is directly executable. So the newer model's attempt to be more helpful counted against it.
Math problems (primality checking): to solve this the model needs to do chain of thought. For some weird reason, the newer model doesn't seem to do so when asked to think step by step (but the current ChatGPT-4 does, as you can easily check). The paper doesn't say that the accuracy is worse conditional on doing CoT.
The other two tasks are visual reasoning and answering sensitive questions. On the former, they report a slight improvement. On the latter, they report that the filters are much more effective — unsurprising since we know that OpenAI has been heavily tweaking these.
In short, everything in the paper is consistent with fine tuning. It is possible that OpenAI is gaslighting everyone by denying that they degraded performance for cost saving purposes — but if so, this paper doesn't provide evidence of it. Still, it's a fascinating study of the unintended consequences of model updates.