Agree with the comments that point out the poorness of Horvat's first step. I think Horvat would admit to that himself. Once he is up to speed he can bull rush ok and is solid enough on his skates to protect the puck and make plays.
Defensively, I think both the stats and your own eye balls point out some important deficiencies.
Defense really starts in the offensive zone and not just inside your blue line. Often it's just as important to break up plays at the other teams blue line and through the neutral zone as it is your end. Horvat is simply not quick enough in transition to provide much of this. You rarely see him tracking down players coming out of their zone or through mid-ice. In contrast, you see a player like Pettersson showing an increasing ability to get in passing lanes on the back check and knocking down passes or breaking up plays. Last year Motte was simply excellent at this and Lammikko wasn't bad. Back in the day, Kesler was an outstanding in defensive transition (Selke like in fact). You watch Horvat and I don't see how you can maintain he is.
And even in his zone, Horvat has significant problems. Tends to take a zonal defensive approach. Basically stays in the mid ice or slot area trying to prevent passes to that area. However, the better defensive players want to get pressure on the puck. You lay back in some kind of zone position, you give very talented players the chance to make plays. The best defensive players are those that are not only capable of getting pressure on the puck but also can get opponents off the puck and, either through their ability to pack the puck or move it quickly, to get the play going the other way. Horvat simply does not consistently apply the type of pressure needed to this. Players like Kesler were and are exceptional at this.
Nor is Horvat is not that effective at shot blocking. Does get in lanes but his timing isn't good enough for him to use his pads well. Ends up getting puck in places were you get injured and also end up deflecting puck towards your own net. One problem is that Horvat goes down and he lacks the agility to quickly get up and back in the play.
Like I said, the stats (particularly his plus/minus - about the worst in the League over his time in the NHL) are poor and, IMO, are a result of his poor back checking, mediocre defensive transition play and his inability to apply enough pressure on the puck in his end. And most of this is consequences of his clunky skating - especially when he tries to quick pivot.