The NYIs made it to game #7 of round #3 and lost 1-0 without their captain Anders Lee, who is their best goal scorer (recorded 100 goals over the course of the last 3 seasons) and is the highest cap hit player at $7 mil AAV, and they also don't have any other $11 mil players still dressed to absorb it.
However what the JT injury did expose is Leafs cap management issues, because when you put all your eggs in one basket of a $11 mil player, when that player is out you suddenly play games with $11 mil less in player salaries/AAV because his replacement is likely a scrub making near league minimum. When you don't top end heavy spend and have 2-3 players using up $11 mil cap then you're better insulated via team depth to absorb a player loss to injury and the gap between him and his replacement a lot more narrow.
Isles deploy a bunch of $5-6 mil players not any $11 mil individual players, and its that team depth of spending cap across many lines of being a deep team with all players chipping in that insulates against just a single injury situation like Leafs did with Tavares.
That holds true also when you have other $11 mil players still playing and they disappear in the series like Matthews 1-4-5 points and Marner 0-4-4 points did when it counts, you can't expect the bottom of your roster making $750k- $1 mil to carry the team and compensate for the high-end salaries, because of a flawed cap management strategy of 4 forwards eating up 1/2 your salary cap. This really got exposed this playoff season both with the players playing and also with those that were injured and out.