When Namek is blowing up Goku gets into one of the Ginyu force ships and sets off to explore the galaxy.
Whilst out there he meets a race called the Yardrat who after some time teach him how to perform the Instant Transmission technique.
In the manga (the comics written before the anime which they were based on) Vegeta never goes on his search he simply trains on earth for the time in which Goku is missing and that's how Vegeta becomes a super saiyan.
The point of the clip you posted is to merely show the moment in which Vegeta realised how to become a super saiyan, to give more of a meaning or more of a reason as to why he couldn't do it before.
It's never actually explained but there are two likely scenarios
- In a state of temporary psychosis at his inability to find Goku and turn into a super saiyan, Vegeta has a Hallucinated epiphany which allows him to see the light (hehe) and turn into a super saiyan.
- It was Goku but he was training with meteors and upon sensing Vegetas Ki he fled back to the Yardrat or elsewhere in the galaxy to continue his training unhindered.
Personally option 1 is more likely, Goku is a lot of things but a liar he is not. He would most likely not have fled Vegeta but have welcomed a fight. He also would have mentioned it when he arrived back on earth.
TL:DR Vegeta went crazy with self induced inadequacies and had an epiphany.
Also the anime creators wanted to make it seem like a bigger deal