Sometimes it does refer to the actual 'open and close' type of gate but not so often. It all depends on when the name was given.Citys and towns became walled in to protect the inhabitants and to allow some control over who could enter. (Why am I reminded of America ?)
Naturally those walls needed the odd opening to allow entry and exit. Of convenience these openings were placed over the existing roadways - then called 'gata'. Over the years the word gata/gate was eventually used for the door itself. A sure sign that the road and not the door is being referred to is when you see the words 'within' and 'without' in the street name either side of the opening. Oldgate Within, Oldgate Without or Bondgate Within, Bondgate without are two of the most common I've come across.
As miners use 'gate' when referring to the roadways in the mines, you can be assured that it's been in use a long time.