The main issue with the two sample sentences is identifying what/where the video was taken from (i.e. the video's source).
- The intrinsic parameters of the camera, from which the video was taken, are not supposed to be available.
In your first example, the parenthetical expression "from which the video was taken" comes after the noun phrase "The intrinsic parameters of the camera", which ends with a noun (camera). Without the commas, it would be natural to take the camera as the video's source. However, the commas make the head of the noun phrase (i.e. the parameters) look like a strong candidate as the video's source.
Simply removing the commas avoids this to a large degree by making the parameters refer to the noun phrase 'the camera from which the video was taken':
- The intrinsic parameters of the camera from which the video was taken are not supposed to be available.
- The intrinsic parameters of the camera are not supposed to be available, from which the video was taken.
In your second example, the portion after the comma dangles without a natural reference. A noun phrase (or simple noun) would be a natural reference, but "The intrinsic parameters ... are not supposed to be available" isn't a noun phrase. While there may be poetic or other literary works that use a similar phrasing, I'd suggest rewriting this instance for clarity.