There is no reference to motion/video found in SC 1.4.3 — simple "images" and "background."
Do the color contrast requirements of SC 1.4.3 apply to text that is in a video and overlayed on top of video footage? My assumption is yes.
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Since your question is specifically about contrast, I'll throw in my two cents:
The WCAG framework is meant to be a set of guidelines as to how to present web content. In terms of reaching compliance, there are very clear criteria (as @JonW points out), and since contrast in video content isn't covered by these, your presumably low-contrast video wont hinder you - but it will be obstructive to users with impaired vision.
Contrast is, as per your assumption, equally important to videos as it is to images and other content, so if we have the opportunity to create content that has accessible contrast levels, we should (and this is where I believe the guideline aspect of WCAG really shines).
In strict terms, no, as even though there may be something that looks like text in the video, it's treated as non-text content as a screen reader isn't able to access it. A video is, in simplified terms (grossly simplified in the digital age!), a series of still images flicked through like a flickbook animation. It would instead fall under 1.1.1 where you need a text alternative for the non-text content.
Personally, I'd still aim for colour contrast compliance because it makes the text in the video easier to read for sighted users. The content is meant to be consumed, and if the text has a good colour contrast against the background it's much easier for people to consume.