It appears that the laws weren't specific to the point of actually using the verbiage to explicitly include "websites" when they were written, but the language used is broad enough to interpret them to include websites. Over the last few years, primarily in California, Florida, New York, and Pennsylvania, lawsuits have been brought against both large and small businesses for not being in compliance according to ADA standards.
It seems to be the case that small businesses have generally been left "under the radar" as the lawsuits have primarily targeted larger businesses and corporations over the years, but these suits could start targeting small businesses a lot more at some point.
Included below are some articles about the ADA lawsuits. There is also a checklist available online to get your website up to ADA standards. It looks like they recommend that companies at least meet the WCAG 2.1 AA checklist requirements to be compliant and avoid possible penalties. Click here for PDF file.
According to one article "if the website has no connection to the goods or services offered in store then the website does not need to be ADA compliant." Though this does not mean that any websites are safe, apparently, from the looks of the research. A second article mentioned that healthcare industry websites are one of the industries that are more likely to be targeted by lawsuits for non-ADA compliant sites. (https://martechtoday.com/is-your-website-at-risk-for-an-ada-accessibility-lawsuit-245172).
Disabled individuals may have many different ailments that prevent them from accessing a website. Individuals with vision, hearing, or physical disabilities makeup approximately 20 percent of the population and will encounter significant challenges accessing websites. As an example, pictures need alternative text for the blind to understand what is being illustrated and videos need to have captions or transcripts for the deaf.
The Web Content Accessibility Guidelines WCAG 2.1 lays out 61 guidelines to follow, as the standard for ADA website compliance. WCAG 2.1 lays out three levels of compliance, A, AA, and AAA. The higher the level, the better your website meets the requirements and allows greater accessibility to users. Currently, all federal institutions’ websites must meet AA compliance on all items. WCAG 2.1 lists all 61 guidelines and says whether each one is required for A, AA, or AAA. AA requires compliance with all A level and AA level guidelines. Accordingly, AAA requires compliance with all A level, AA level, and AAA level guidelines. Since the law is still murky, web developers recommend meeting AA compliance like federal institutions.