Update: This is no longer needed.
The .NET Core 2.0 is released now, but the AWS Elastic Beanstalk Windows AMIs do not yet support it (only 1.0/1.1 is supported), so if you're using AWS Toolkit for VS 2017 you can't (successfully) deploy .NET Core 2.0 projects.
While waiting for Amazon to update them (not sure if they are going to do it, especially since .NET Core 2.0 is not LTS for now), I devised a quick fix that requires minimal changes to the project and does not require any AWS interaction. Feel free to use it until AWS upgrades the subject AMIs.
If dotnet/core#848 is resolved, the easier way using "packages" key will be available.
Also, a small recommendation on AMI selection -- do not use Windows Server 2016 images for these kinds of deployments, you gain almost nothing, but the antimalware tool that is installed by default impacts performance too much. I recommend to use Windows Server 2012R2 Core AMI (ami-1bfa1a63 at the time of writing).
P.S. I know that Azure deployments are easier, but their "security measures" are developer-unfriendly.