I know the movie is fiction, but this doesn't mean they had heavy technology in Tony Stark's past days. So how did he record this hologram?
He recreated it based on his memories of the event...it's not an actual recording made at the time.
As I recall this was demo of new technology not a replay of the event.
It' s called Binarily Augumented Retro-Framing (B.A.R.F.) that "hijacks" the hippocampus to clear traumatic memories.
From the Wikia
The B.A.R.F. relies on an implant installed on a pair of glasses that connects with the user's hippocampus, allowing it to find a certain traumatic memory and alter it before projecting that memory onto an external infrastructure.