I believe it means that if you add 10 points to speed, the cooldown will halve. So going from 10 speed to 20 speed would mean that all their abilities refresh in 1/2 the time. At least that's what I've been assuming, but I haven't paid close enough attention to notice the difference for sure.

That's correct. Technically, speed is a multiplier, displayed in units of 10.

So:
10 speed = 1x base cooldown
20 speed = 2x base cooldown (1/2 the time)
30 speed = 3x base cooldown (1/3 the time)
40 speed = 4x base cooldown (1/4 the time)

> That's correct. Technically, speed is a multiplier, displayed in units of 10.

So:
10 speed = 1x base cooldown
20 speed = 2x base cooldown (1/2 the time)

---------

But speed 11 still has a benefit, right? I don't have to wait until the speed = 20 before there's a payoff?

For sure. The underlying variable is a floating point multiplier, so 11 speed represents a speed multiplier of 1.1x.