This is a bit tricky, because unlike Now there doesn't seem to be a way to tell Hyper to "build this Dockerfile and deploy the resulting image". They expect you to build a container and publish it to a registry instead.

https://docs.hyper.sh/Reference/CLI/load.html allows you to publish an image directly from a tarball, but that still leaves the challenge of creating that image. The nice thing about the Now integration is that you don't need to have Docker installed on your local machine.