...the full and equal enjoyment of the goods, services, facilities, or accommodations of any place of "public accommodation" by any person who owns, leases, or operates a place of public accommodation. Public accommodations include most places of lodging (such as inns and hotels), recreation, transportation, education, and dining, along with stores, care providers, and places of public displays.
You are correct, ADA defines an “employer” as any person who is 1) engaged in an industry affecting commerce; 2) employes 15 or more full-time employees each work day; and 3) for at least 20 or more calendar weeks in the year. In the context of physical spaces, ADA would not apply to companies with fewer than 15 employees. However, courts don’t seem to have come to a consensus on what digital compliance really should look like. Because websites can be accessed anywhere in the country, small business owners might potentially face lawsuits in unfavorable jurisdictions. If you are a small business owner, I would recommend consulting with an accessibility lawyer and ask what they recommend.
This is the reason why I think web design firms have to position themselves as solution providers and not just web guys/gals. A client doesn't need a website, they need sales. The website is just part of that solution but it's not the solution and unlike web design, service like email marketing automation, SEO, and PPC requires an experienced professional.