It's 1994, and both Sheldon and President Hagemeyer would know that Dr. Stephen Hawking had not been a regular figure at Caltech for 20 years and thus would not be a big reason for Sheldon following through with the move there.
George is excited when he's told that Rice University may be interested in him as a football coach, and he describes them as a "great college". Rice is a highly ranked academic-oriented school, but their football team is always in the lower third of the rankings. They are somewhat known for their baseball though.
In The Tam Turbulence (2018) both Tam and Sheldon mention that it was the intention of both of them to go to California and Sheldon got mad that Tam decided to stay in Texas with his girlfriend. It seems that that has been retconned so that Tam was never even apart of the move to California in the first place. However, seeing as Sheldon completely ignored Tam during their last lunch, it's plausible that Sheldon made up their agreement in his mind as he is known to be an unreliable narrator of his own life.
When Sheldon visits this comic book store for the last time as he leaves to look at t shirts the camera clearly shows on the comic rack a DC Futures End comic which was an event that took place between 2014 and 2015 over 30 years AFTER this episode is set.