I take this ferry a lot and it is a bit small. We (parents) prefer to go overnight but the kids love a day crossing despite the limited activities on board.
Definitely ask about a cabin when you get on. We always book one (usually about £30-40) and take it in turns to have a nap away from the kids! Or to let them nap, watch tv, have a shower etc.
There is a small basketball court (caged!) on the deck. Obv a basketball might be a bit much to carry, but you could burn off some energy there, perhaps twice - that could kill an hour or so.
There are a couple of Playstations in the seating area next to the shops - we've often found one isn't working, so if you plan to use them, be on early and get your turn in first or prepare to wait a while.
There is usually a family friendly film on a big screen between the Playstations and the 'soft play' bit (absolutely tiny but DD loves it). There is a small table area with some toys for younger children and older siblings sometimes hang around there, so he may make a friend there.
The cafe/bar area (at the end where you exit onto the deck) is also nice and does Chocomel hot chocolate. Usually has TVs with sports or something on.
We spend quite a lot of time outside at either end of the crossing - watching the coastline disappear, seeing what we can spot, and same again other end. You could see if you can spot any wildlife and have a bet about what time you will first see land.
Harwich and surrounding areas is not big and many travellers go straight on from the port without stopping, but it might be nice to find out about the area you're travelling from - see if DS can find historical/literary references (e.g. it's mentioned in Dracula, the boat from The Boat That Rocked film is docked in Harwich Town and you may still be able to visit). You could plan to have a short time in Harwich Town before embarking. There is a Lidl, Morrisons, Starbucks, McDonalds etc at a fairly new retail park area just before you reach the port, so you could easily grab a few bits and a coffee before you embark.
Edited as realised you're travelling the opposite way from what I'd thought!