Whether he deserves to be in the HOF or not, let me say this in defense of Horry. His strength... his specialty... was much more than hitting game winning shots. There are often certain moments that can change the outcome of a game. It might be a matter of stopping a catch-up run, turning the momentum in your team's favor, silencing the crowd, taking away the opponents' will, or giving hope to your own teammates and getting them back into the game. But a lot of games turn on just a couple of plays, and everyone in the arena can feel it when those things happen. A block or a steal on one end, and a 3-pointer on the other, maybe draw a cheap offensive foul, and suddenly the whole game feels different. Robert Horry always had an uncanny sense for those moments.
People used to say that he shifted gears in March. But he shifted gears in individual games - just when it would do the most damage to the opposing teams. Game-winning shots always make the highlight reels. But what a lot of reporters (and fans) tend to forget, is how often Robert Horry was the reason that the game was close enough to win with a buzzer-beater. Or how often he kept the other team from making a game close enough for them to possibly win with a buzzer-beater of their own.
I have a mental image of Horry scoring a basket, and then shambling down the court slowly - and suddenly turning to steal the in-bounds pass and dunk it. I've watched him do it a dozen times or more (probably many more) and it always demoralized the other team. He could turn a 10 point lead into a 5 point lead in a couple of seconds, and make the other team start pressing to make their own shots.
The last-second shots were just one aspect of Horry's real talent - he knew how to cut the heart out of the other team. He knew just when to do something special - but he also had the ability to actually make it happen. If it were only a few times, it might be luck. But he did it repeatedly, over the course of his whole career. That's one of a basketball skill.
And yes, it did translate into championships. Houston probably wouldn't have won either of those rings without Horry. (I watched A LOT of Rockets games in those days.) For instance, in the 1995 Finals, the Rockets won 120-118 in overtime. People remember that Nick Anderson missed 4 free throws, and that Kenny Smith made the late 3-pointer to take the game to OT. But they forget that the Magic jumped out to a 20-point lead in the first half, and that it was Robert Horry's 5 blocks and 3 steals that shut down Orlando's momentum long enough for his team to climb back into the game. Without him, Smith's shot at the end would have been moot. Of course, it didn't hurt that he nailed back-to-back 3-pointers to open up the overtime. That game killed the Magic, and the series was basically over as soon as it started.
If there's not a special place in the HOF for Horry, maybe there should be. It's sort of like when Bill Bates played for the Cowboys. He made such a difference on special teams, that the NFL actually added a spot in the Pro Bowl for a special teams guy. Bates got inducted into the "Madden Hall of Fame", because Madden recognized how a guy like that could change the outcome of a game. He will probably never be in the official NFL Hall of Fame, but Madden understands just how valuable Bates was to those Superbowl teams. If there was a Madden Hall of Fame for basketball, Horry would definitely be in it.