The question doesn't assume an ordinary video camera. In fact, it calls for a "special video camera".
If I extend the definition of camera to a more generic sense of light sensor with some sort of recording mechanism, you can get a near-continuous feed, rather than a discrete one. You can think of a single photo-transistor as a degenerate case.
In this case, you'd have to spin the disc faster than the sensing element can detect the light level, the electrons to transmit that info, a buffer to store the previous light level, a comparator to indicate a change, etc.
You'd have to be spinning the disk at ludicrous speed for that to be an issue.
In the case where continuity is an issue, you'd likely need 2 cameras near each other since you wouldn't likely be able to spin the cameras near enough to the disk speed to be able to infer direction from that.
Also, with 2 cameras, you can eliminate some buffering and increase the maximum RPM you can reliably detect.
Then again it didn't specify the camera needed to determine the direction, it only implied it... I can look at the spinning disk and determine the direction with 0 cameras for a wide range of sizes and RPMs.