Being that Behavior is a game development company, is it feasible that they used in-house libraries for developing common game functions, such as animation, that could explain some of the similarities?
And if that's the case, and Behavior had ownership of the libraries prior to their contract with Bethesda, does usage of these libraries in Fallout Shelter therefore transfer ownership to Bethesda?
With APIG+Lambda you get CloudWatch integration 'out-of-the-box', and can expand the metrics and logs you send out with a few added lines of config.
You can also toggle X-Ray for a detailed view of your call graph.
If the default implementation isn't good enough, you can define your own CW events, alarms, and log filtering.
I'll grant you that you can't just ssh into a host and tail some logs, but if you're keen you can send your logs to elasticsearch for a better arbitrary search experience.