Aztecs are very capable of any victory path. Domination obviously is very easy for them. Furthermore, as stated already in this thread, they are superb on defense, too, so the peaceful victories come just as easy compared to other civs.
Temples giving science means you get cheap early science even in inland cities that focus on production. This bonus allows Aztecs to keep up with other scientific civs. Don't forget the temples' original purpose--culture--so science is advanced while GP will be attracted to your civ and stopping your cities from converting or even flipping a city later in the game. Generally Shakespeare's Theatre won't be built by others, but you can take advantage of this and put one in your city. It counts toward your 20 and generates more GP. More pop means more culture, so pumping a mega city also benefits a cultural city with Shak's Theatre.
Once you get to modern age, +50% gold means you buy whatever the heck you want. If going for culture, buy wonders and spies to steal GP from other civs. More versatile than Russian trait. If domination, buy units obviously. Equivalent to 1/2 price units. If tech, buy temples, libraries, and universities, and even courthouses. Once you have Space Flight, buy all the components and win in a few turns. If economic victory, set all cities to focus on gold and go from 0 to 20,000 in 10 turns or so. Store hammers in another wonder while you build up 20k to open up World Bank, then switch from the wonder to W. Bank.
(I don't know if you get the heal if you choose the retreat option, I never needed to).
