It eschews docker, and Dockerfiles and their non-determinism, and builds the layers itself, and uses a python lib [1] to push and pull container images.
In order to ensure reproducibility/determinism, however, Bazel doesn't have an equivalent of the RUN instruction. You have to use other Bazel rules to fetch and produce artefacts and add them to an image, and there aren't always rules for what it is you want to do (I have a spot of bother with installing pip packages, for which there is apparently alpha support).
This is, I think, the thing with Bazel: it has to re-invent everything to ensure this reproducibility and hermetic seal, because it doesn't trust existing build tools to do this, and quite rightly so if this is what you're seeking. But I suspect it's going to be painful doing things outside the mainstream supported stuff.