dotcommunism can clarify BUT now I read this again, IF Mittelstadt were to sign with the Sabres now, the contract would be a 2017-18 season contract. Casey was 18 as of September 15th of the 'signing year' which I think is 2017-18, I know you are assuming it's 2018 but that makes no sense at all. Had Casey been a CHL player, he would have signed an ELC over the summer, the team would have sent him back to junior, his junior team doesn't make the playoffs so we call him up for some games at the end of the season, it would be under 10 games, so his contract slides.
It doesn't matter what season the contract was signed, only the calendar year matters. In 2018, Mittelstadt turns 20. He's not eligible for a contract slide regardless of the season the contract takes effect.
what would be the rationale for this rule? it penalizes the Sabres for having an NCAA player rather than a CHL player, the CHL kid can play 9 NHL games in his draft +1 season and the NCAA kid can't without the team losing an ELC season. makes no sense.
The whole point of the slide rule is to allow teams to see if a player is ready at the start of the season and if he isn't allow the team to return him to juniors without burning an ELC year. Yes, players can be called up after their CHL season is complete, but that doesn't happen very often (because good players are often playing in the CHL playoffs and there's usually little reason to call such a player up to the NHL vs the AHL when their CHL season is complete).
Regarding the point of the rule (why players who are 19 as of September 15, but turn 20 before the completion of the year aren't eligible for a contract slide) it's because such players are eligible to play in the AHL the year in which they sign their SPC, and they don't want contracts sliding for players who were always slated for the AHL that season (that's not the point of the contract slide). As for how it specifically affects Mittelstadt it's an edge case that's the result of a confluence of circumstances.
Also another interesting wrinkle is that if Mittelstadt signs an ELC that commences this season, he would have four seasons of waiver exemption (including this season), meaning that he would be waiver exempt for one season following the completion of his ELC.