IIRC, exhaustion doesn't work (properly?) in OT, so think about it that way. If you had an "advantage", you lost it on OT.
I lost a game similarly on BBM because of it. They get some rest and they're back to how they were when the game started (or so it seems). Exhaustion also doesn't carry between games, so it is what it is.
I'd addapt what you suggest to "I feel like exhaustion should have a bigger effect on teams with poor Game Shape".
7 player lineups are not considered short rosters, (although they still had 2 of 5 starters exhausted). They are in a grey area as you can see by some players exhausted but not all. Also they are risky because fouls and injuries could cause major issues.
In summary, the changes to prevent short rosters were specifically geared to 5 or 6 players playing the entire game with no downfalls.
I don't know enough about either teams' players to comment about the match, but the ratings were pretty similar for both teams, so a close game seems to make sense.
A full season roster of 7 players is, IMO (and in reality I believe), a short roster. That team has 7 players on its roster, so if that isn't short, that's not very realistic (though it's the game is entitled to choose to be so or not, of course).
A team that consistently plays the same 7 players should be more prone to injury and "wear and tear" or ineffectiveness, if you will (as the accumulated effort should start taking its toll during the course of the season). The GE also doesn't seem to consider "exhaustion" based on players that play big stretches with small rest, regardless of total minutes. I've seen games where guys play like 22 out of 24 minutes but they don't show any signs of getting tired/ineffective or alike.
So, basically and IMO (of course), ehxaustion is a very small factor, especially in teams that avoid it by small margins. I believe there's room for improvement there.