The first disallowed goal was a league initiated review. It wasn't a coach's challenge. The puck can deflect off a skate into the net, but you can't attempt to play it off your skate into the net. The phrase that gets mentioned is "obvious kicking motion". I don't think the Calgary player meant to do it, but it's clear that his leg goes from behind him to in front of him - extending forward from his body. The puck goes under the goalie pads as a direct result of being deflected from the skate extended forward. The league judged that this was a kicking motion.
The second disallowed goal was a coach's challenge for goaltender interference. Goaltender interference is a really vaguely defined thing, and a failed challenge would result in a Calgary power play. The Stars review guys are very good at making these calls. Here, they had a couple of points in their favor. First, the Calgary player's leg and skate was fully inside the blue painted area that defines the goalie crease. While it's not the be-all-end-all, if you contact the keeper inside that paint when you don't have the puck in your personal possession, you're likely interfering. Second, that contact prevented DeSmith from moving to his right to play the shot. The Stars had a good argument to overturn the goal, and the league agreed.
This game was a practical "must have" for Calgary, and they played like it. They were the more energetic, aggressive team. Hockey is ugly when you do all that, and sure-thing goals are swatted down by a sliding DeSmith, and Harley playing keepy-uppy with the puck. The Stars followed that sequence with a drive, a slick side pass, and a double rebound goal to go to 4-2. Calgary thrashed themselves at the net, but the Stars are a contender who have seen it before.