Other way round. He invented the induction motor (1887) which the three-phase grid was then demonstrated to drive (1891). That's how influential it was. There are other reasons a three-phase grid is handy but being able to drive these brushless contraptions must have seemed utterly wild at the time.
A three-phase grid cannot drive a two-phase induction motor, like that invented by Tesla.
In 1891, the three-phase induction motor was invented by Mikhail Dolivo-Dobrovolsky, combining the principles of the three-phase synchronous motor previously invented by Mikhail Dolivo-Dobrovolsky with the principle of the induction motors invented by Nikola Tesla and Galileo Ferraris.
Like any inventions, the induction motors of Nikola Tesla and Galileo Ferraris had not sprung out of nothing, but they were based on the experimental observation that had been known for many decades that if you rotate some magnets around a disk of copper, the disk will rotate, even if the magnets do not have any action on the disk when stationary.
Because of the symmetry, it is easier to generate electromechanically three-phase currents than two-phase currents where the phase difference must be precisely of one right angle.
