Your comment existing has a carbon footprint, doesn't mean it should be paired with the dairy industry's

Yeah. But since farm animals are often fed from farmed plants these days, animal-based tends to be worse by quite a solid factor. This article puts butter at 4x worse than margarine, for example: https://www.forkranger.com/blog/is-margarine-a-sustainable-alternative-for-butter/

How plant-based compares to this new process still needs to be seen for sure. If it's just a machine you can plug in at the store and everyone can get their butter like out of an ice cream machine, without transport and cooling chain, then it's likely a lot better.
But at this point, I don't expect the process to be much more efficient than what plants are doing, which means you'd still need a ton of energy and particularly also land area for it.

Plus the simple effects of land conversion. Plus the emissions from the feces.