By that definition, chess engines would have free will, as they would be able to search a through larger amount of possible moves given the extra time and thus find another move.

The problem with that definition is that time itself is an external input of sorts. Therefore, everything is not the same since you have +k time. Your definition would also apply to many trivial decision processes, e.g. a computer programme that randomly switches between each possibility and picks the one it ends on when the allotted time has elapsed. I doubt that programme would be considered to have any will at all, let alone free will.

Sure, its probably a better definition of "free action" but I am very convinced that those are necessary conditions (though probably not sufficient). Additional time can be an external input, that's fine, its only important that its the _only_ one.

Any definition of free will that doesn't appeal to dualism will allow programs to have free will, that's just par for the course.

There's no such thing as just internal inputs though, because those inputs are there because of external factors from the past. They're permanently entangled. If the universe is deterministic, the results of that experiment were always going to happen.