I'll be honest, I don't really see much of a difference. FlyBMI was placed into administration, Loganair took the bits they wanted and the rest of the company was left in administration.
I'm not an legal expert so I don't know the ins and outs of a TUPE claim but there does seem to be a reasonable amount of evidence that there is a transfer of business and it's not simply a new airline hiring pilots out of work.
However, from reading the notes on the LHR slots appeal what sticks in one's craw is Thyme OpCo (laughably) arguing they only shut down the old airline to rid it of it's business liabilities because they thought that was what the CAA wanted and preferred. They even suggested if they had realised that would mean they would lose the slots they would have looked into other restructuring methods - presumably pumping enough working capital into the airline to keep it afloat.