Our first Princess cruise was when our kids were 10 and 12. Electronic devices, movies on the stateroom TV, and the kids club were their favorites. I would advise taking your own cards and travel games if you want to be sure there is something you can play together. Everything on the ship is variable. We've now been on 5 Princess cruises with our kids and every cruise is different. They loved the naturalist for Hawaii, they hated the naturalist on board for Alaska. Sometimes the comedians are hilarious and pre-teens loved it, our last cruise had a boring comedian. One time there was a magic show my boys loved.
With COVID and cruising being so unpredictable, I wouldn't count on the cruise line to provide entertainment outside the kids club. We've done two cruises with Princess since the restart. The entertainment crew was obviously struggling on both of them due to sickness, under-staffing, and last minute changes. There probably will be something your kids enjoy but I have no idea what that might be. We'll be doing another cruise in less than a month and while I know we're going to love it, I also have no idea what to expect based on our last two cruises.
ETA: Alaska specific things my boys enjoyed. Eagles - we loved watching them and looking for them in the trees while docked. We also went to the eagle sanctuary. Whales - we took binoculars and watched them off the ship from our balcony, also went on a whale watch excursion in Juneau. Glacier Bay - NPS rangers come on the ship and they bring junior ranger books so the kids can get their badge. Salmon berries - we went to a national park that had something to do with totem poles, my kids had no interest in the totem poles. What they did love were the salmon berries at the edge of the bay. The park ranger took my kids out there, pointed out the berries and picked some for my kids to eat. There was a crowd of about 10 kids out there picking and eating salmon berries. That was the highlight of the day for my kids.