This is 'One Step from Earth' by Harry Harrison.
It's a series of short stories about matter transmission. At the start it's established on Earth, and the first story covers the first gate sent to Mars.
Stories include putting a gate in Jupiter, space battles fought to stop a gate being used for an invasion, an assassin escaping via a series of gates and rediscovering a planet that has been cut off for centuries.
The last story 'a Tale of the Ending' is as you describe, with two characters talking and visiting various worlds, discussing why they use base-12 numbering, and implying that they had taken over from a previous sentient race (indicated to be humans).