The double success came the day after Red Bull boss Mateschitz passed away, an event that Horner suggested made Verstappen even more determined to win.
The Dutchman looked set to score a straightforward victory until an 11-second pit stop due to an issue with the left front dropped him back.
He thus had a fight on his hands, but he quickly moved up the order and eventually passed Lewis Hamilton for the lead to score a record-equalling 13th race win of the season.
“I think that Max was driving a very controlled race today,” said Horner. “And then it all came alive when we had a gun issue on the second stop for Max, and we'd already elected to go on to the medium, which we felt was the better tyre.
“And he lost close to probably eight seconds in the pitstop. Which put him behind Charles [Leclerc], and then obviously he had to close down that gap down to Lewis. And it was almost as if it had been scripted for him to have to come back through the field.
“I think Dietrich would have quite enjoyed that race from above to see us overtaking Mercedes with five or six laps to go, and win the constructors’ World Championship. I think he would have been very proud about that race today.”
Regarding the wheelgun issue he said: “We've had it once in a practice. It's gone into quarantine. It'll go through its process, and we'll find out what happened.”
Horner said Verstappen had to be patient and pace himself after the frustration of the long stop, but his recovery was helped by Red Bull's stronger pace on the mediums while Hamilton was stuck on hards.
“I think we were probably more competitive on the medium than we were on the hard. So that was why we went back onto the medium at that second stop.
“And his pace, obviously, at the back end of the stint was then strong enough to really take it to Lewis, who looked like he was sliding the car, pushing the car very hard.
“So it was a game of patience. And I think Max was able to quickly get his frustration under control leaving the pit lane and not cook the tyres but bring them in, make the pass on Charles and then hunt down Lewis.
"The one opportunity he had was decisive and he got the job done.”
Given the sad circumstances Horner felt Verstappen was extra determined not to settle for second and hunt down Hamilton for the win.
“With 10 laps ago I'm not sure it would have been the result that we would have all hoped for if we'd have finished second in the race today," he added.
"I think Max had a determination going into the race. And I think he was always going to go for it.
“And we made life difficult for him today and made it more entertaining for the crowd. But he did it in the best possible way, and to win the grand prix here, to seal that constructors' championship, was a very special moment for us as a team and as a company.
“And to do it on a weekend where lost Dietrich - obviously we'd like to dedicate this championship to him and his family for everything that he has done, not just for Red Bull Racing, but also for F1.”
