Have I understood it right?
It does this because flywheels hold momentum but as angular momentum. The inerter converts linear motion to angular momentum. The gearing also it to give the same effect of an enormous inertial mass without itself being massive.
My understanding as to why this is useful is as follows. Suspension works best when the vehicle is heavy and the wheels are light. Imagine a battle tank on ultra strong bicycle wheels: the tank would glide along as the wheels jump up and down over every dip and bump. Something similar happens when you drive home with a car load of paving slabs.
Having a massive vehicle is a huge penalty though for other reasons. Battle tanks are not nimble! The only thing you really want the mass for is as an inertial mass in the suspension system. For accelerating and going around corners you’d rather it wasn’t there at all.
Donut Media actually has a great video on the topic: https://www.youtube.com/watch?v=t58qjcNwEbo
As far as my understanding goes, it's basically a low-pass filter that also provides momentum in the direction of movement - this actively dampens spring oscillation (as opposed to a shock absorber, which passively dampens oscillation). It should be installed in parallel with the spring and shock.
Analogous to a capacitor being the inverse of an inductor in an electrical model.
Trying to find a better mechanical analog to the capacitor to optimize a passive suspension was the motivation because mass-damping suspensions had already been banned when active suspension got banned.
But I probably misunderstood the video.