How do you define 'work'?
In the case of royals, it's not like they receive a payment at the end of the day, so that in itself makes it different to most of us. Kate will enjoy her lifestyle whether or not she 'works'.
But you seem to be suggesting that just because something might be enjoyable, it can't be 'work'. Yes, many people would give their right arm to be at a Wimbledon final, and I'm sure Kate will enjoy the match, but she will also be under great scrutiny and has official duties to perform as part of her role as patron of the AELTC. So yes, there is an element of 'work' involved, even if it's nothing like what most of us would consider as 'work'.
When Margot Robbie wears a dress worth thousands and poses for photos at a glamorous film premiere, is that 'work'?
When Gary Lineker sits by the Brandenburg Gate and talks with his mates about the sport he loves, is that 'work'?
If Kate didn't like tennis, would it be 'work'?
Does it really matter?