What is the mechanic in Settlers that enables this? Can't think of anything apart from how resources seems to be unevenly used throughout the game (wood and brick being more sought after early on to build roads and settlements, while iron and grain become more important when cities are built later on).
If you trade with the winning player, they win faster. If you trade with players who are behind, it doesn't really change the outcome of the game (they will probably still be behind at the end of the game)
The only thing preventing that winning player from reaching 10 points is 2 stone and 3 wheat. So as long as no one gives the winning player those resources, the game continues.
Alternatively, the winning player can try to win on their own by massing up 20 other resources and trading 4 for 1. But everyone else can more efficiently get the resources they need by trading with each other, allowing for an innate comeback mechanic.
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At a minimum, that puts even the weakest players always in the position as kingmaker. So everyone has something to do at all stages of the game.
In Catan there are multiple ways to try to get to 10 points, so if someone else is in the lead via one strategy (e.g. city building) it's still possible to be in the lead for a different one (e.g. development cards).
Catan is a poor example, because there is no built-in mechanic. Player interaction allows for targeting leaders and making mutually beneficial moves with people who are trailing. For everything great about Catan, it's a pretty old Eurogame, and it lacks a lot of refinements to the genre that have been made since.
Power Grid gives a turn order advantage to players who make less income.
Dominion is a deckbuilding game where you earn victory points by buying and keeping junk cards in your deck, so your deck gets worse as you score increases.
Suburbia reduces your income progressively as your population (score) increases (which also forces players to balance the two).
A number of games including Terra Mystica give turn order advantage to whoever passed their turn first in the previous round.
There are, of course, many more games that don't have such a mechanic, but rely on balancing the relative rewards of the various moves such that early turns are less about taking a lead and more about setting up which paths to victory you can attempt in later rounds, so the skill is in setting up a path that you're able to execute well and then executing it well.
The main thing is the free-for-all nature combined with the existence of trading. It is obviously tactically incorrect to trade with anyone who is about to win, but it usually takes a while to get that last point or two without a trade.