Yeah, looking at their contract chart from 2008 makes me realize this is accurate. Hasek was the only notable UFA on that 2008 team, they only lost him, Drake (retired) and some guy named Hartigan.
Outside of UFA's and retirement the other absences were:
Andreas Lilja - Got a concussion after getting KO'd in a fight with Shea Weber a few days before the trade deadline. They initially thought it was short term (otherwise Holland might have gone out and gotten a rental dman), but he ended up being out for an entire calendar year.
Darren McCarty - He started 08/09 as basically their 13th forward, but went up and down from GR to Detroit because with their cap situation they couldn't carry 23 guys when everyone was healthy. Then he missed a few months with a groin injury. Once healthy, he never played for Detroit again, as he had rightfully been passed on the depth chart by Abdelkader, Leino and especially Helm, who everyone knew would be a regular once the playoffs rolled around.
That said, and more to your point, it's arguable how much impact, if any, those losses had. Outside of two wins, Hasek was a non factor. The skaters were all bit parts, Lilja a 3rd pairing/PK dman, Drake and McCarty were 4th line wingers and Hartigan was basically a spare center. The only element missing from those guys would've been experience, as most of their replacements were rookies for 08-09:
Lilja -> Rookie Ericsson, who provided similar size/physical play
Drake and McCarty -> More minutes/responsibility to a technically still rookie Helm - Kopecky (who was hurt for the entire 2008 playoffs) - Rookie Abdelkader (who took over for Kopecky after he went down and missed the rest of the 09 playoffs) All of whom provided grit/physical play
Hartigan -> Rookie Leino (although IIRC, Abdelkader filled in more as the 5th center while Leino mostly played winger)
Hilariously enough, I think an arguement could be made that the better team lost in each finals due to injuries. 08 Malkin was playing with broken ribs, and in 09 the Wings had Hossa with a torn rotator cuff, Datsyuk nursing wrist and ankle injuries looking like a shell of his usual self, and Lidstrom literally having to get stitches for a Torn Scrotum (not kidding/trying to be funny) after Sharp nut shotted him in the WCF
That’s 3 of Detroit’s 4 best players, and another valuable performer, Franzen, had Gary Robert turn his brain to mush.
The Red Wings were also missing Kris Draper for most of those playoffs, who despite his age, was still one of the better 3rd/4th line/PK defensive centers in the league at the time. IIRC, Datsyuk and Drapers injuries overlapped, which means the Wings were slim down the middle without two of their best FO and PK centers, and caused them to have to go with Helm and Abdelkader at 3C and 4C respectively. I think Draper was still hurt when he came back against the Pens as well.