Wacky racing games are a genre that we usually don’t get in North America- probably a localization thing. Paris-Dakar Rally Special, until now a Japan exclusive, is now available in English and it is certainly in the “wacky racing games” genre. The interesting thing about it is all of the similarities between this 1988 title and what would eventually become Grand Theft Auto.
I am not 100% positive but I believe Paris-Dakar Rally Racing is the first racing game that allowed you to exit the vehicle to explore the surroundings. This can include buildings, rivers, under bridges, etc. Sure, you cannot attack other people while on foot (like in Grand Theft Auto) but you can shoot bullets from your vehicle.
In Paris-Dakar Rally Racing every level is unique. One level may have you avoiding a platoon of tanks while another may have fighter jets searching you out and attacking. GTA has yet to implement those things as far as I know.
Grab the English patch for Paris-Dakar Rally Racing from ROMHacking.net, unfortunately, the full game is not freeware so we cannot link directly to it.