Because AWS is already deeply embedded in the games industry. Where do you think all of those multiplayer servers run for big AAA titles? This is probably just a move up the vertical for them.
Does anyone but Star Citizen use it Amazon Lumberyard?
Unity and UE4 really are the current leaders in game engine technology, CryEngine, while great, has suffered in the last four years or so and isn't a significant competitor.
If you look in the link there are six games listed. One is Star Citizen, two are (afair) by Amazon game studios, so that would leave three other games. No idea if these are just the show cases or all of them.
So, not the greatest uptake, but Amazon was always willing to give things time to mature. We'll see if they can take market share of UE4/Unity.
Integration with AWS products. And I assume Amazon is developing a game engine that integrates well with AWS products in order to sell more AWS products.
Big networked multiplayer games have people distributing lots of data to each other: device controls, ship maneuvers, text and voice comms, other such. Servers and bandwidth become huge issues and AWS is the most advanced and scalable platform for all that right now.