No cups in general would be a point against the GM I agree in this particular case I do not.
We're talking about awesomeness, not about mere goodness.
By your logic, Dean Lombardi is an awesome GM. Two Cups (2012, 2014), two conferences titles, six playoff appearances in 11 years. But the LA Kings have known only inconsistency in this time. I'd hardly call him an awesome GM.
What about Mike Gillis? 1 Conference title, 5 division titles, 5 playoff appearances in 6 seasons. Pretty darn good, until you realize he managed the Canucks after Dave Nonis, and is pretty much responsible for the basement status they are in right now.
Let's not forget our good friend George McPhee, most recently of the Capitals (he's now with the VGK). 1 conference title; 7 division titles; 10 playoff appearances in 17 seasons.
You want awesome GMs? Ken Holland, Red Wings. Sure, they missed the playoffs this year, but 20 straight seasons under his eyes in the playoffs? Legendary. Along with 3 Cups.
Lou Lamariello, when he was with the Devils: 5 conference finals; 9 division titles; 21 playoff appearances; and 3 Cups. Right now, he's putting together the Leafs for a long tenure, and seems to be doing a damned good job at it (although, $6.25M for zombie Marleau? Not so sure of that, but the man holds every damned offensive record for the Sharks).
And, of course, Stan Bowman, Blackhawks. 8 seasons, 8 playoff appearances, 3 Cups. Enough said.
Stevie Y isn't in the conversation with the latter 3. With the former 3, he has a similar record. His team isn't a consistent threat. He's also made questionable choices:
He traded Bishop for a 4th round pick. The Stars now have him. Bishop was instrumental in that Stanley Cup Final you were talking about. Now, they have to rely on Vasilevskiy, whose record was good enough last year to keep the Lightning away from good draft picks, but not good enough to get into a weak Eastern Conference.
The team's scoring forwards lack depth. Kunitz isn't going to help you score points, even if he has a lot of experience.
The team handled the Drouin issue poorly in the 2016 season. Thankfully, they handled it better this off-season, picking up Sergachev. Otherwise, Stevie Y's first-round picks have been up-and-down (where's Connolly, DeAngelo, and Howden?).
So, no. I put Stevie Y in the "he's pretty good" category. Not awesome, but not Burke infamous.