There are a few answers to this, but the main point is that the definition of force refers to an interaction between (at least) two objects. In General Relativity, what happens instead is that one object curves space, and another object then freely moves within the curved space, so that it's no longer a direct interaction.
Having said that, gravity is still not fully understood, and General Relativity is certainly not the final explanation of gravity. In a more complete picture, it's expected that gravity will be explained in terms of a new particle, called the graviton, which then directly allows two bodies to interact. No complete description of a graviton exists, and none has ever been observed. But, if it were, then it would put gravity back on the same footing as the other basic forces (electromagnetism, and the strong and weak forces), because all of those also have "exchange" particles, eg the photon is the exchange particle of electromagnetism.