It prohibits countries from claiming sovereignty over territory beyond Earth, but the colonies themselves can still be sovereign. Assuming the treaty continues as it is it just means that countries won’t be able to draw borders around vast lifeless regions on Mars or the Moon and claim jurisdiction over them, they’ll still be able to build cities there and the cities will be theirs to control.

Treaties like these lapse or get amended over time as the realities of life make them obsolete, though. I expect that once there are cities on Mars there’ll be borders as well.