The Busy Beaver problem is one of the most theoretical, one of the most purely mathematical, of all theoretical computer science questions. It is really about what is possible in a very abstract sense.

Working on it did make people cleverer at analyzing the behavior of software, but it's not obvious that those skills or associated techniques will directly transfer to analyzing the behavior of much more complex software that does practical stuff. The programs that were being analyzed here are extraordinarily small by typical software developer standards.

To be more specific, it seems conceivable to me that some of these methods could inspire deductive techniques that can be used in some way in proof assistants or optimizing compilers, in order to help ensure correctness of more complicated programs, but again that application isn't obvious or guaranteed. The people working on this collaboration would definitely have described themselves as doing theoretical computer science rather than applied computer science.