Short answer: No.
Long answers: The definition of Alpha male is pretty much the leader in it’s simplest form, the person that everyone looks to for guidance and who they follow instruction from. The requirement to lead in the wild would have been determined via fighting, this is no longer true. Here for example of what is a less stereotypical but very Alpha males by today’s standards.
Thinking about his life the innervation he brought forward. Yes he’s a Nerd and yes he is rich. But he built one of the most successful company of all times and beta’s simple do not do that. Yes he is smart, but without being a risk taker innovative. And yes their might not be stories of him screwing super models, and his wife might not be that hot now. But just take a look at his daughter:
She must have been pretty damn hot in the past to produce that. Take a look at Bill and see how he tallies up against the Alpha male traits page.
Having said that Alpha often are in very good shape, how physically fit you are usually means that you show some of the traits that are listed under the how to be an alpha male page. To become physical fit you need to understand what actions effect your fitness levels (dietary requirements, the amount of exercise required and the correct type for your goals) this show a high level of understanding yourself. Also once you understand it you need to actually do it which requires a lot of will power hence becoming the master of yourself.