All authors have to be entrepreneurial if they are to succeed in finding an audience and having the effort be financially sustainable. Not all authors publish to get a return on the books, most people who write never make any money at all from it, they do it for promotional reasons, or as a complement to another activity, or to help an audience understand something that is challenging to comprehend.
All entrepreneurs could benefit from being authors although most will never spend the time to learn the craft. I read that Jeff Bezos requires people who attend a meeting, to draft their thoughts first and bring in the writing with them. I completely understand his rational, if forces people to structure their thinking. It is a cultural bias he is imposing within Amazon, it works for him but it isn't for everyone. Some of the best entrepreneurs find it very challenging to have the concentration to write, they are better at speaking or kinetic activities, or deep listening, or visual representations. The cognitive styles of entrepreneurs can vary and therefore while being an author could be beneficial for some, it is not for all.
What entrepreneurs and authors do have in common, is they both struggle with editing, they are good at creating the material, the words, the product, but editing is a special and difficult skill. As an entrepreneur I am constantly asking, how can I make the product simpler, as a author I ask can I explain this easier. In both cases I prefer the creative process of building up the material but the real value comes in the editing process. Like entrepreneurship, writing is not a solo activity, it needs a team, editors, publishers, marketing folks, similar to entrepreneurs, they are made by the team they assemble for the work at hand.