First racing game experience was with "**MOTORRACE"
That was in about 1969 I think. Might have been 1970.
It was played on an IBM Call\360 timesharing system using IBM2741 typewriter terminals. IIRC, up to 8 players raced together.
The game was a synchronized turn-based game, with each player entering three numeric parameters at the prompt. The prompt read "G,B,A", standing for gear, brakes, accelerator. I think there were 4 gears, and B and A could be set to 0-9. Single digits speeded up inputs, no commas required.
Once all players had entered their "move", the software calculated the outcome for the next slice of time (maybe 5 seconds, I forget), and replied with a cryptic representation of player speed, position relative to each other and next corner.
Any player who arrived at a corner during a time slice was asked to provide new values for B and A for the remainder of the time slice, thus enabling players to brake into corners and accelerate out. Gear changing mid-corner was not allowed.
Despite the clunkiness of the concept and implementation, players became very excited when the racing was close. There was only one track, and one type of car. Before racing, it was possible to print out a map of the track. Each corner had a maximum speed limit which, if exceeded, would cause the player to spin out and suffer a time penalty.
Advanced players tinkered around with combinations of braking and throttle to tweak acceleration and deceleration so as to arrive at corners at the optimum speed.
The game was written by one developer.
I guess there has been some improvement in racing games over the years, but it has always been fun!