Because companies very rarely make purchases of this size with cash, it's almost always a combination of financing, stock and cash. Why spend your own money when you can spend someone else's, especially with interest rates at record lows?
There are a hundred different reasons why Amazon wouldn't do this but financing isn't one of them
Right, but they already have razor thin profit margins. Let's just say that they do somehow manage to buy the division; with all that added bloat, what would the profits look like then? I'm not saying it's impossible, but it seems like a huge risk for Amazon. Why take that huge risk when they could take a much smaller one (build their own Android based console), which may turn out to be much more profitable in the future?