Two possibilities: The Earth rotates at about 465 m/s at the equator. This video's measurements could include that speed, though I don't believe so as it starts from 0 m/s.
Most likely it's because the rocket is traveling in a horizontal arc during its travel.
Rockets trying to reach orbit need to reach a horizontal speed of around 7.8 km/s in addition to the height. In fact, the vast majority of a rocket's energy to get into an orbit is horizontal movement, as reaching the height necessary to get into space is comparatively easy.
By the time the rocket first stage passes its apogee it still has significant horizontal velocity to burn off, which is why it's still traveling at 300 m/s~ at that time.
Here's a visual example of the flight profile (not to scale) of the Falcon 9 Drone Ship landing
And an example of the profile with a return to launch site landing
(Source: Space.StackExchange.com post)
Some further interesting information, include a GTO Profile (One where the rocket first stage does not return to a landing site) can be found in the SpaceX Falcon 9 User's Guide on the SpaceX website.