The evidence was presented on Tuesday during the second day of a preliminary hearing in Provo, Utah, in which prosecutors are trying to convince District Court Judge Tony Graf to bring Tyler Robinson, 23, to trial.
Investigators allege he shot Kirk from a rooftop at Utah Valley University while the right-wing activist and ally of President Donald Trump debated with students.
Robinson faces seven criminal charges, including aggravated murder. Prosecutors plan to seek the death penalty.
Utah investigator David Hull, testifying as the video was shown, said the images were recorded as the shot was fired, "and the individual then stands up and then moves across the building to the north".
Hull identified the person as Robinson.
The hearing, expected to last all week, is the first public test of prosecution evidence concerning Kirk's September 10 assassination, one of a series of attacks that have intensified concern over US political violence in recent years.
Erika Kirk, his widow, was in the courtroom on Monday and Tuesday.
Hull testified that surveillance videos showed Robinson making contact with representatives of Turning Point at the university on the day of the shooting. Videos all show him investigating access to the building from which the shot was fired and having lunch at a campus fast-food restaurant.
In the early hours of the next day, a police officer stopped a vehicle Robinson was driving and took down its licence plate number, Hull said. The encounter took place before law enforcement had identified him as a suspect, Hull said.
The defence tried to raise doubt that Robinson was responsible by suggesting someone else may have been involved.
On Tuesday, for example, defence lawyer Kathryn Nester asked Hull about a handgun found in a backpack on the campus after the shooting. Hull responded that the handgun was not determined to be evidence in the case.
Robinson turned himself in to police the day after the shooting. He has not yet entered a plea. His lawyers have yet to comment on his guilt or innocence.
Kirk, a co-founder of the conservative youth organisation Turning Point USA, was credited with energising many young voters behind Trump's campaign to regain the presidency in the 2024 US election.
Prosecutors are expected to present further evidence they say ties Robinson to the shooting, including statements he made to friends and relatives and DNA tests linking him to the alleged murder weapon.
