You could argue that at it's peak Bell labs was a vanity division. That research may have changed the world, but very little of it likely ended up benefiting AT&T in any major way financially. It's telling that once AT&T was broken up Bell labs, while existing in some form for years after, was never reestablished.
Markov chains form the basis of n-gram language models, which are still useful today.
Markov chains are also the basis of the Page-rank algorithm.
Hidden Markov Models (which are just an extension of Markov Chains to have unobserved states) are a powerful and commonly used time series model found all over the place in industry.
In the pre-deep learning model Markov chains (and HMMs) in particular had very wide spread usage in Speech processing.
They are probably one of the most practical statistical techniques out there (out side of obvious example like linear models).