Fly to Mars (or anywhere else in the solar system), land, unload passengers and cargo, refuel, take off again, fly to Earth, land. Refuel and start loading for the next flight.
That's the end goal. And since not all bodies SpaceX may want to land on have a comparable atmosphere to Earth, parachutes are not part of the plan.
This isn't the vehicle that's going to do all that, but they have to start somewhere to build the tech that eventually will.
More like: launch to earth orbit (dropping the first and second stages, that land at spaceports for shipping home and refuelling), dock to a larger ship (nuclear?) which carries them to Mars, un-dock in Mars orbit and make a powered descent to the colony there. And then do the whole thing again backwards.
I doubt this vehicle will be used for landing on Earth(why not use parachutes?). I would rather send it to Mars orbit and reuse it there as a landing module, but not take it back to Earth.
Why not use chutes? Because with rockets, you can steer, and fine-tune the rate of descent. You don't need to splash down at sea, you can land on solid ground, and pick which bit of ground to land on (such as a spaceport). It's less of a bumpy ride and cheaper to recover.
The auxiliary solid fuel rockets of the space shuttle slashed in the sea with parachutes and were "reusable". But they were so bumped that the refurbishment procedure involved a lot of handwork and iirc more than a month.
That's the end goal. And since not all bodies SpaceX may want to land on have a comparable atmosphere to Earth, parachutes are not part of the plan.
This isn't the vehicle that's going to do all that, but they have to start somewhere to build the tech that eventually will.