Maybe there is an element of triangulation in that, but it's far less precise and ambitious than GPS.
Once you know which tower the phone is connected to, coordinates of that tower, antenna pattern, and distance (from timing advance and speed of light), you can calculate approximate cell phone location.
You get more data if the phone moves or propagation changes and phone changes towers. In urban environment with many towers location obtained this way can be very precise. Not as good as GPS, but good enough to within a block.
This is a simplification. Real systems also use signal strength, take into account multipath propagation, and apply some filtering from physical constraints (how fast a cell phone can move).
Your link is for GSM and states a 550 meter resolution, but I tried looking up LTE and I think it said 10 meters there.
I also understand modern (maybe next generation) towers will use directional transmission to avoid sending signals in all directions. Even if that's a 20° beam, that narrows don't the location by a lot.
The only substantial difference is that in case of GPS the calculation happens on the receiver side (GPS signals only go in one direction), while cellular service providers calculate time advance on the tower side.