They are definitely a PE firm. They buy up struggling companies with the aim to revitalise them, or otherwise recoup the cost of investment+ profit. They have switched to mainly relying on traditional debt rather than outside investor money recently but that doesn't make them not PE.

In fact this is much like the older form of PE, where efficiency gains were the main objective.

Bigger PE firms now usually focus on roll-up strategies (buy loads of similar companies and merge, say car washes is big right now for example, as well as dental, vet and family doctor/GP practices) as well as utilising bucket loads of leverage to amplify gains. This does not however make what bending spoons is doing not PE.