Is it possible to build a steering system without using gear racks such as part 87761?
It's possible to build a steering system without using a gear rack. Rack and pinion steering is simply one of the easiest ways to translate the rotational motion of a steering wheel to the translational motion needed to adjust the wheels.

Here's one example of using tie rods and a knuckle to accomplish steering:



That's obviously quite complicated because it incorporates suspension as well as steering, but it's too pretty to not include. This basic concept is what is often used on go carts because it's dead simple, and mechanical advantage isn't very important on vehicles that small:



This design can be simplified to not need ball joints as long as all the moving parts stay in the same plane. Here's an example of Ackermann steering implemented that way:



You could swap 6575 into that design instead of 2825 pretty easily.

Here's an even simpler example with a motor mounted perpendicularly to avoid even needing to use any gears: