The sensor in your camera has about 18 megapixels, and all those MP are used to record pictures and movies. What's different is how the sensor data was processed on the picture and the movie.
For the picture you scaled down the original 18MP picture using Photoshop, GIMP or similar. This was probably a high quality scaling operation, so the resulting 2MP image still looks pretty good, since it was generated from the whole 18MP of data.
For the movie, it is the camera that did the scale down operation. The camera has to scale down images at a rate of 24 per second, so it can't use as good scaling as you get from an image editing app. I'm not sure what the algorithm is, but I'm certain its main goal is performance and not quality.
For the image you took a raw or a lightly compressed jpeg (not sure which one you used). If you went with the jpeg, it's got 4.7MB worth of data. The raw is way more than that.
For the movie the camera compressed all the frames using H.264 encoding and you took a random frame from the middle of the movie. Your movie has 58 frames and is 20.3MB big, so on average, there are just 360KB for each frame if we consider the audio and metadata in the noise. H.264 makes an amazingly efficient use of the limited bitrate by encoding differences between frames, so it isn't as bad as it looks.
So based on the above reasons, I think the picture vs. movie quality cannot be expected to match.