Rachmaninoff was notorius for making cuts in all of his music, both recorded and live. Here's a letter he wrote to Medtner about the Corelli Variations:
"I've played them here about fifteen times, but of these fifteen performances, only one was good. [...] And it's so boring! Not once have I played these all in continuity. I was guided by the caughing of the audience. Whenever the coughing increased, I would skip the next variation. [...] In one concert, I don't remember where - some small town - the caughing was so violent that I played only 10 variations (out of 20). My best record was set in New York, where I played 18 variations..."
The composer editted the 1st Symphony, 1st concerto, 4th concerto, and 2nd sonata by making large numbers of cuts. He complained about the vast length of much of his music many times - he once said of his second sonata:
"I look at my early works and see how much there is that is superfluous. Even in this sonata so many voices are moving simultaneously, and it is too long. Chopin's Sonata lasts nineteen minutes, and all has been said."
Quotes aside, it's pretty evident that Rachmaninoff was never wholly confident or secure with his own playing, at least on the outside. The speed at which he plays the third concerto suits the piece perfectly well, and the cuts were probably just made on the composer's whim. (This is the only recording he ever made of the piece. The only pieces Rachmaninoff recorded more than once are the second concerto, the G minor and C# minor preludes, and one or two of his polkas).