Well, there are two sides to this.
First, many will argue that the CONCEPT of the hotel is VERY "Disney". The monorail going through the hotel, the "futuristic" A-frame design. It's all very retro-Disney. The hotel itself is not what I would consider contemporary, though.
The rooms are very modern, and sort of remind me of the W hotels (if you are familiar...look it up online and look at some pictures of the rooms...very similar decor/feel). The rooms ARE contemporary, and not Disney at all! In fact, consider the Garden Wings or the Bay Lake view rooms in the tower. From inside the room, the only HINT that you are in a Disney hotel are the toiletries in the bathroom. Now, if you get a MK Tower Room, then I don't think it gets much more Disney than having the MK in all its splendor RIGHT outside the window! Plus, the view of the Seven Seas Lagoon, GF, Poly, and the ferry boats and monorail are about as "Disney" as you can get. But again, you'd have to have the window open.

Close the window drapes, and you are back in, what I consider, a very classy albeit sterile hotel room.
The Contemp is a huge convention hotel, so there are a lot of people there on business all the time. There are families there, sure, but it sort of lacks in the "immersive theme" that, say, the Polynesian, Wilderness Lodge, and pretty much the rest of the Disney hotels pull off very well. You won't get this feeling of being "someplace other than Disney World" while at the Contemporary. You'll get the feeling of being in a very nice hotel right next to the Magic Kingdom.
I'll say, I've stayed there twice, but not with children. Now that I have children, it would honestly be my last choice of all the Deluxe Resorts. I don't feel that there is much for younger kids there. The pool, although big, is blah compared to the other deluxe resorts. There is a huge lack of grassy spaces and landscaping in general. It's all a huge concrete playground, and that is not very fun to me. I would choose ANY other Deluxe before the Contemporary until my kids are much older, in their late teen years, which seems to be a good age to enjoy that resort.