Several hoofstock species are only visible from the actual safari (addax, forest buffalo, banteng, Przewalski's wild horses, dromedaries etc.). There is an option of taking a safari bus for those who aren't able to do the drive themselves, but it only runs from October to March...so you might want to look into the car option. If you look on the map available on the website https://d33b12c77av9bg.cloudfront.net/originals/safaripark_beekse_bergen_plattegrond_2024_nl.pdf you can see for yourself what you might miss. The orange route is the drivethrough safari.
You can see the forest buffalo from the walking safari (although some luck is needed as they prefer to hang out at a spot near their stables that's only visible from the car safari) as well as the wild horse (from the lemur enclosure/ bird arena) and the addax/dromedary (behind the okapis, but only if they are in that part of the enclosure)
Some animals that you can see on the car safari can also be seen by boat, but you'll need some luck and the views won't always be good. Those are red deer, axis deer, Pere David's deer and banteng. The only animal you will defenitely 100% miss out on if you skip the car safari is the sika deer.
To sum it up: If you skip the car safari you will miss sika deer and have less chance to see red forest buffalo, ostrich, addax, dromedary, red deer, axis deer, Pere David's deer and banteng. (note its also possible to see dromedary in one of the savannahs of the resort, in the background when you are looking at the giraffe enclosure from the walking safari)
Everything else should be good.
Source : I work there