I feel that in the case of .NET Core claiming that the changes were cloud-focused is valid. After all, .NET was already in place and Microsoft didn't really need to make it that modular. It did do it and it spent a lot of resources doing it, in order to follow its cloud strategy.
Beyond the modularization efforts, one could look at the Linux port and dramatic performance improvements in the same light.
In contrast, the "old style" was to setup a physical server manually: install the OS, install all the dependencies for your application, configure everything manually. If you need to scale out or replace a broken server, you repeat these steps. There are of course various levels of automation that can be done with this, but dealing with physical severs meant at least some manual effort was always required.
In this case, I read "cloud optimized" as you can easily deploy to the typical "cloud" server instance or container (which is basically an installed OS with enough config to get it on the network). Your application doesn't have any dependencies: for example, .NET Core (framework) is bundled.