He signed his extension a year and a half ago, before his draft year even started. Nobody, likely including Stutzle himself, thought he'd be an NHL candidate as an 18 year old.
And that the Draft would be held in October thereby missing the August 15 cutoff. as per
The Athletic’s Corey Pronman: “a player with a valid European contract for the 2020-21 season cannot be signed to an NHL contract after Aug. 15.” The signing window apparently opens again at the end of the DEL season. Do we know of any europeans playing e.g Raymond, Holtz, Lundell that have signed ELCs?
Pronman's thing confirmed by Daly
"NHL deputy commissioner Bill Daly confirmed to Pronman that this would remain true for this year. The signing window would reopen whenever the player’s respective international federation released him, be it at the conclusion of the player’s team’s season or, if he is invited to the IIHF World Championship, at the conclusion of that tournament. These rules are designed to give European teams roster certainty once a season is underway."
So the path of least resistance is to just let him play in the DEL this year.