CSP applies to the page containing the code, not the code. In your case, this means that the client pages may or may not have content security policies which allow (or don't allow) your script to run based on it being a third party script.
Your script can't influence those - that's kind of the point. CSP is designed to ensure that only known scripts run, or known elements are able to be loaded by the page.
In the case of a video player script, the hosting site (the one which loads your code) would need to allow your script, and for the appropriate types of files to be loaded from your servers if they implemented CSP. You may need to look at CORS to enable access to content from your domain by your script, which is running in the context of the client site, although this depends on what you're doing with it - if you're just including a video file using a
<video> tag, this probably isn't needed.