As I discussed previously, every game has different victory conditions. However, many games, especially points-based games, also have different paths to that victory. Take 7 Wonders. It’s a drafting game where players win by building the best city states, either by constructing the most beautiful buildings, having the most advanced technology or having the biggest army.
Why would designers create multiple paths to victory? Well, for several reasons.
Replayability. Some games, especially short ones, become tedious if there’s only one strategy, because then, winning just means doing one thing better than everyone else. (Note: luck and bluffing based games defy this rule.) However, providing several strategies to win allows players to mix and match, creating rather different experiences each game. One example of this is Sushi Go, where players make different combinations of sushi in order to score points; however, each type scores differently, and thus players are have to decide quickly which strategy to adopt.
Domination breaking. Sometimes, one player is so far ahead it’s not funny. Having several paths to victory mitigates that problem by allowing players to use other strategies to topple the dominant player. Alhambra does that well, as, in that game, players score points by having the most tiles in particular categories. No player can get them all, and this allows every player to have one (or two) building types that they have the most of, which, of course, allows them to actually score points.
One note: unlike other mechanics I’ve discussed, this is not as widespread across games; however, it’s effective in increasing replayability, as you can literally make a new strategy every game and still win.
However, like every other mechanic, this should only be included in a game for one reason: does it become more fun with it?