I think it has never been fully explained how the address system for the Destiny gates works. At least I don't remember it being explained in full detail in the show and I didn't find a complete explanation in the wiki.
There are a few things however, that we know about the gates:
- They use 7-symbol addresses with 36 possible symbols (see wiki chart)
- The symbols do not represent constellations but seem to be an ancient numeral systems
- They have a limited range (SGU Season 1, Episode 15 - Lost) and cannot dial galaxy-wide much less intergalactic (presumably because they lack an external power source)
- They communicate with each other and Destiny using short-range subspace signals (SGU Season 2, Episode 17 - Common Descent)
- They can only be dialed using a remote, there is no actual manual dialing
Additional you have to consider that the modus operandi for the seeded gate networks is entirely different form the (mostly) fixed transportation networks established in the Milkyway or Pegasus galaxies. These were specifically designed to solve the logistical problem of transporting people and goods over interstellar and sometimes intergalactic distances. Because any gate can theoretically freely dial any other gate, they needed a fixed address system that everyone can use.
The gate network set up by the Seed ships however, was only meant to be used by Destiny's crew. They seeded gates on planets of interest either scientifically or because they could provide valuable resources needed to replenish supplies and maintain the ship. They are also only seeded along Destiny's travel corridor and not everywhere inside a galaxy. They can only be dialed using a remote because they were set up for the specific purpose of giving Destiny's crew access to the planet and then let them go back once they're done. It's pointless to have a memorable address because they're unlikely to travel to that planet more than once. While the gates provide a simple and limited network functionality, they were never meant to provide a permanent network.
They couldn't use constellations and had to use an abstract address system because they needed a generic system that works in any galaxy Destiny travels to. In order to make this work they configured the network to keep itself updated via short-range subspace. Each gate in range is aware of any other available gate in range and also it's address and maybe even it's relative position.
From SGU Season 1, Episode 15 - Lost we can reason that addresses are probably unique. Eli not only easily recognizes Destiny's address (also this might be a special case), later on another planet he also recognizes the address of a planet they visited in an earlier episode. This can only be possible if the address is exactly the same as it was when they dialed it from Destiny. As such it seems that each gate has it's very own address regardless of point of origin. What we do not know is if they are unique across all seeded gates (seems unlikely because all seed ships would have to be perfectly synchronized to keep addresses unique) or if they are simply unique within a limited range, like within a galaxy.
This still doesn't exactly answer the question how Destiny can successfully dial a gate with the strange address system. But maybe this address system also works entirely different. As far as I'm aware Destiny is never shown to establish a connection with a gate outside of it's range (Earth being a different topic) despite being capable (given enough power) to make intergalactic connections. It should certainly be able to connect a gate somewhere in the same galaxy. But they never do. In the aforementioned episode Lost Destiny sends a team that goes through several planetary gates trying to find their lost crew members. Who do exactly the same. They don't try to just dial the gate from their previous stop, presumably because they can't.
Which leads me to the following conclusion. I think the gate address of a Destiny-era gate only serves as an identifier, not as coordinates. It only serves to identify a specific gate and Destiny already knows the exact position of the gate from the subspace communication received from said gate. Destiny can't dial gates out of communication range because it doesn't know if the gate is still there.
As far as I know Milkyway and Pegasus gates do not communicate with each other via subspace with the exception of establishing an actual connection. This system his much more suited however, to provided up-to-date information to the Destiny which is just traveling through.