Well, I'm sure HKS understands how a suspension works, but I'm not sure he was clear enough.
The spring is the whole "structural" member, it supports the car in compression or tension. It would "work" (supporting the car) even without a damper.
What a spring does is to "dissipate", or to "blurr", the effects of the irregularities of the road on the wheels.
The damper is used to dampen (duh...) the movements of the chassis. If you don't have a damper, the spring would oscillate "too much".
How much is "too much"? Well, in racing cars the idea is that, together, spring and damper work to keep the wheel in contact with the road.
Normal cars also use suspensions to keep passengers comfy, but this is in conflict with the "wheel-in-contact" idea, so...
"Wheel-in contact" means that the wheel transmit some load (some weight) to the road, without any "rebounds" (hopefully).
This transmitted "weight" is what gives grip to the wheel. Is this "weight" what allows you to steer, brake or accelerate.
Imagine you have an R/C car without a suspension: with a "hard chassis", the car will jump as soon as it hits a significant bump in the road, won't it?
If this "suspension-less R/C car" is on a curve and it jumps in the air, the wheels will loose traction and the car will slide.
So, the idea of suspension is to avoid that kind of jumping to offer the driver a more or less constant grip.