Transfer of ownership isn't even required, since it was open source code hosted on github. All someone needs to do is re-host the files, and wait for the DMCA notice to push back on it.
True. It should also be possible to maintain it outside of the US, where the DMCA doesn't apply. In some European countries Mazda probably wouldn't have a lot of options to take it down.
Usually you can't go after people for creating content, even if it's a copyright violation. They also can't "uncreate" it, they can't delete the concepts from their brain. You can only stop them from publishing/selling it.
In this case the code was on GitHub before, so they wouldn't even need to give the code to the new target entity, this entity could just copy it from an undisclosed person who has a copy.
The tool Mazda is using is DMCA. That applies explicitly to whomever is hosting the content. More specifically, it applies to whomever Mazda sends the DMCA notice to.