Assuming school's out there will be plenty of other kids on any Alaskan cruise for the kids to interact with. We sailed HAL, NCL, Celebrity and all 3 had excellant kids programs with many activities. For ship size HAL Zaandam was the smallest of the 3 and there was no crowded feeling at all.
Yes, there are video gaming and movies. There are also basketball courts, ping pong, swimming, golf nets and/or golf simulators.
We enjoyed the food on all 3 lines in the main dining rooms, including NCL which seems to get panned a lot on these sites.
On our 3 cruises they had none of the pool games that warm weather cruises seem to have....bellyflop contests, etc. That was a plus for us.