When I played the game, I saw the "Hypergate" tab on the Starbase, but I took it as an ancient map to find the other Starbases. So I used the Starbases as a place to refuel and travelled the long way there with my ship. I used the Starbases to extend the reach of my ship by refueling there. I still managed to win the game but I spent a lot more RU than I should have.
I realized there was a teleport feature, when I saw a video on Youtube of someone playing the game. Oh !
I think perhaps the Starbase should mention to the player when he goes on this tab that the Starbase can transport the player instantly to another Starbase. The Precursors had advanced tech so I'd expect more user-friendliness from the interface.