There was some influence, but mostly to cover their butts legally
There was a computer version of Advanced Civ that closely followed the board game and there still exists an online version of the game (rol) Civ :: (rol) Civilization Log in
Having played both extensively, I’d opine the civ pc game has nothing in common with the boardgame besides the general theme of “pilot the demo/mil/tech advancement of a civilization competing against others” ; and if you squint other general game design ideas like “tech goes faster the more people you have” or “population increases faster when it’s spread out”
Note that Mega Civilization (which plays up to 18 and cost north of $200), decided to break into two games (East and West) to make it more affordable/approachable. (each plays 5-9)
Just about the time they ere going to release the West they got into a legal problem with the trademark. They eventually renamed the game Western Empires (and will introduce Eastern Empires later).
Even though Mega Civ was released I think it is now named Mega Empires. https://westernempires.com/faq/