For discussion’s sake – while I don’t know the specific nature of your videos, my guess is that they might be demonstrating various techniques or other content in which simply hearing the audio of the video wouldn’t deliver the full context of the content. If making that content accessible is something you’d want to do, you’d likely want to start with a written description of what takes place in the video. Beyond that, high contrast vector images or diagrams showcasing specific parts of the technique would certainly help.
As you’ve probably figured out by now, the answer is no, because it’s not at all clear how or even if ADA rules will be applied to any particular website. Still, it’s generally a good idea to err on the side of caution. Many states have adopted their own accessibility laws, and the volume of accessibility-related lawsuits filed against websites has ballooned in recent years. Plaintiffs have been more successful in these suits than ever before. With no clearly defined regulations to follow, it is probably not worth it for most companies to gamble that a court will rule in their favor.
The fastest, most certain way to be sure your website is in compliance is to contact a qualified web design agency and have them perform an audit of all your online properties. Make sure you interview the agency thoroughly first, as not all agencies are up to speed on ADA website compliance rules. A qualified web design firm will be able to identify any violations of ADA Website Compliance and outline a plan for updating your online content and properties.
If you do get sued, if you immediately remediate your website, you may be able to get the lawsuit dismissed on mootness (there’s no longer anything in dispute, i.e. plaintiffs are arguing your website is inaccessible but you’ve already made it accessible). This definitely does not mean you should wait to fix your website but it does mean you may have an out.
The words in the tag should be more than a description. They should provide a text equivalent of the image. In other words, the tag should include the same meaningful information that other users obtain by looking at the image. In the example of the mayor’s picture, adding an “alt” tag with the words “Photograph of Mayor Jane Smith” provides a meaningful description.