This is why saying "they switched engines" inaccurately describes what has happened. I'll break it down. StarEngine was based off CryEngine 3.7 with some cherry picked 3.8 updates. Lumberyard is also based off CryEngine 3.7 with some custom tools, a few updates, and integration to things like Amazon Web Services. StarEngine has been using Google cloud services (competing with AWS) for a while now (to a pretty decent expense).
Aside from price Google's could services have a large disadvantage if you want to build your globally available online video game - servers that are only physically based in the US. AWS has global server clusters with high speed datalinks between them, bypassing some country's issues with internet connectivity (Australia for example). AWS will allow worldwide players to connect to a server semi-locally and use AWS's high speed dedicated links to interconnect with the rest of the servers that will be running CIG's gameplay server software. Currently non-US players (especially those across the Pacific) have not so great latencies due to having to connect with US based servers at Google.
So, it's nothing that their engine wasn't "doing" before that they are throwing out. By adding Lumberyard's AWS integration to StarEngine, they now have access to those resources. They also have engineers at Amazon that will be helping them migrate their gameplay servers (already done) and make future improvements as SC evolves. AWS is free for smaller projects and more competitively priced than Google on larger projects. It's also almost a certainty that CIG got a good deal on using AWS for slapping "Lumberyard" on their splash screen.
I feel I've had to say this next sentence a lot on this subject, but I'll say it again for clarity: They have not switched engines. All of the work they did before is still there. The only bits that have been "thrown out" would be how they were interfacing with Google's could services since the different companies utilize different APIs and architectures. They have taken the AWS integration code (which is a module within CryEngine's structure) and dropped it in place of what they had before for interfacing with Google. I'm sure there's an interfacing module between the two to do any API translation required, but it's unlikely since AWS already uses CryEngine for Lumberyard and would be used to its built in calls.
Instead of switching engines, they changed web services providers. Lumberyard has other components they're interested in as well, supposedly integrated Twitch support.
I hope that was clear. Nothing was thrown away except Google.
Engineers helping design scalable server software to work on a complex cloud infrastructure. Amazon has invested a lot in that arena (something Crytek never did, so CIG has been on their own thus far; also Amazon has spent more than CIG have taken in on developing AWS, around 2400 employees and billions spent). Their expertise will be invaluable to what CIG are trying to do. AWS has pretty good off-the-shelf cloud server software, but it's not intended to do what CIG are building. Amazon's engineers will be helping with that side of it (server side) while CIG continue to manage the core CryEngine code they've been working with and building for years.