Not at all! In fact, it is actually better if you only make one video that is applicable to all the jobs you are interested in.

When you submit an application for a job, the manager receives a link to your profile.  Any updates you make to your profile afterward will also be updated in your application. This means that the manager of each job you apply for will see the same video. Your video should be generic enough that it will be relevant to all the jobs that you apply for.

If you want to tell the Hiring Manager anything, in particular, you can send a cover letter. This cover letter will not appear on your profile and will only be visible in this one application.