You're right, talent levels will typically dictate salaries in the NHL. However, if these stats become official and start to inflate player totals, they could potentially affect contract bargaining.
For example, Pavel Datsyuk scored 97 points last season. Credit him with the 4 shootout goals he scored and he ends up with 101 points, a significant scoring milepost.
So you say Datsyuk was gonna get paid anyway because he's one of the best. Fair enough, but let's look at Radim Vrbata, certainly not a superstar by anyone's definition and not necessarily someone you'd expect to see in a shootout.
Yet there he was at the end of last season having scored 5 shootout goals. Not only did he perform better than an established superstar (Datsyuk, along with others), it pushes his season goal totals up to 32. Again, 30 goal scorers typically get paid at a higher level than 27 goal scorers, so it could affect Vrbata's bargaining position come contract time.
Compare him to Mike Knuble, who had 29 goals last season (and 55 points, Vrbata had 56). Knuble had zero shootout attempts, thus zero shootout goals. Was his season substantially better or worse than Vrbata's? Doesn't seem that way unless you add in Vrbata's shootout goals and he becomes a 30 goal scorer.
It's an admittedly slight shift in perspective, but enough that it could potentially cost a guy like Knuble a raise simply because he didn't get to shoot in a shootout.
By the way, nice to meet you, Mr. Devil, I'll be your Advocate in this discussion.