The alpha particles close to the nuclei were affected by its charge, but the vast majority of particles shot at the gold foil went straight through. What did Rutherford conclude because of this fact?

An underlying assumption of this experiment that is not always appreciated is the infinitesimal THINNESS of the gold foil. Malleability refers to the ability of the material to be beaten into a sheet. All metals are malleable, gold is extremely malleable amongst metals. A block of gold can be beaten into a foil only a few atoms thick, which I think is quite phenomenal, and such gold foils/films were used in this experiment.

Rutherford could only account for these phenomena by proposing an atomic model in which MOST of the atom was EMPTY space, and a small, massive, nuclear core contained most of the mass of the atom. The nuclear age was born.

Also see this old answer, especially as it contains Rutherford's reaction to his experiment.

Rutherford came to the conclusion that the bulk of an atom is made up of empty space, with a dense, positively charged nucleus at its core.