But he was served penalties in game (for roughing, not fighting, I think?). The question is whether his conduct broke rules to the extent the league can step in and issue supplemental penalties. As a Caps fan, you get pretty used to the circumstances in which suspensions can occur over the years and I'm not aware of that being one of them? But happy to be proven wrong, because I'm really not defending that conduct at all.
If what Wilson did calls for supplemental punishment under the CBA, he absolutely should be dealt it – reputation or not. If he isn't eligible for it, him being Tom Wilson shouldn't make him an exception to the rule. But in that circumstance, the league would need to urgently address that problem ahead of next season, because I'm really not comfortable with what happened at all and no-one else should be either.
Short answer, yes.
Long answer, yes, the League can step in and apply supplemental discipline on any play, at their discretion. Their ruling of supplemental discipline does not need to match the call on the ice at the time of the play, and in fact, there does not even need to be a call on the ice.
This allows the DoPS to make the ruling they deem appropriate with the benefit of multiple angles, slow-motion, player and referee interviews, testimonials, and defenses, and without the restriction of missing the play, having an obstructed view, other incidences happening at the same time, game management, etc.
This falls under Rule 28:
[T]he Commissioner may, at his discretion, investigate any incident that occurs in connection with any Pre-season, Exhibition, League or Playoff game and may assess additional fines and/or suspensions for any offense committed during the course of a game or any aftermath thereof by a player, goalkeeper, Trainer, Manager, Coach or non-playing Club personnel or Club executive, whether or not such offense has been penalized by the Referee.
As the DoPS has the carte blanche, players then have the right to defend themselves during a supplemental discipline hearing, or to appeal after a decision has been made (Wilson himself appealed a 20 game suspension back in Sep. 2018, as you'll likely remember, and had it reduced to 14. The suspension was such a large number of games less for the incident on the ice but because of his history.)
As per the Rulebook
Fighting involves "at least one player punches or attempts to punch an opponent repeatedly or when two players wrestle in such a manner as to make it difficult for the Linesmen to intervene and separate the combatants ... The Referees are provided very wide latitude in the penalties with which they may impose under this rule. This is done intentionally to enable them to differentiate between the obvious degrees of responsibility of the participants"
Aggressing involves a "player who continues to throw punches in an attempt to inflict punishment on his opponent who is in a defenseless position or who is an unwilling combatant ... A player who is deemed to be the aggressor of an altercation will have this recorded as an aggressor of an altercation for statistical and suspension purposes"
Roughing involves "Roughing is a punching or slamming motion with or without the glove on the hand, normally directed at the head or face of an opponent"
All three of those rules were broken, and DoPS has the right to enforce discipline on them, regardless of any call on the ice.
Agressing was last used in a suspension last season on Zach Kassian, and in 2018 on Alex Burrows.
Roughing is frequently given as a fine, but has been used in a suspension in 2019 on Milan Lucic, and in 2018 on Maxi Domi and Tyler Bertuzzi
Interestingly, there's also this, which technically could also be applied to both teams
Fines and Suspensions – Clearing the Area of a Fight - Failure by players (or goalkeepers as required) to clear the area of a fight shall, in addition to the other penalties that may be assessed, result in a fine to the team of $1,000 and the Coach of said team in the amount of $1,000.
I don't think I've ever seen that applied publicly though (could be something they apply privately without a press release from DoPS, since it's technically an automatic fine).