Getting 13m isn't taking the whole increase. It's taking his percentage of the increase.
For example, if the cap was increasing from 100m to 110m, a player signing for 15% would get 1.5m of that 10m increase, and the team benefits from the other 8.5m.
Marner was never overpaid, and he's not a "dud" in the playoffs by any measure, advanced or not. Even by just production, he's been the best on the team, and is one of the better playoff producers in the league. Not equalling the production of some of the highest playoff producers in NHL history for very obvious reasons that you choose to ignore does not make one a dud.
While the gap is not as big as it once was, Marner is still easily the better player. There's more to a player than goalscoring. Paying Marner 12m would be paying Marner less than Nylander. 13m, and even higher, is in no way ridiculous, and there is zero reason to believe that Marner is going to "fall off a cliff" anytime remotely soon. In fact, he's likely to last longer than most players, considering how he generates his impact. Nylander is probably the biggest worry in that regard, with how he relies on speed.