The VPAT® you linked to is quite common. It's a Voluntary Product Accessibility Template, typically placed somewhere publicly available on the product/company website or filled in on request if a potentially selling/tendering/pitching to a US government agency.
Since 2017, WCAG 2.0+ forms the basis of the Section 508 accessibility conformance, which VPAT 2.0 (and beyond) aligns with. Older VPAT versions had quite a different format and, I have to say, a much greater opportunity to be circuitous or less direct (perhaps deliberately ambiguous!?) in the way a question was answered. VPAT 2.x allows much less scope for ambiguity, asking you to state how a product meets or does not meet criteria.
Having said that, if you are not intending for US Federal procurement, then you can still use the VPAT and complete it at a level of detail that suits you. You don't necessarily have to complete the AAA section anyway. If you look at for example, Google Drive's or Docs VPAT (both are PDFs), they are much less decorated than your example.
You can complete the VPAT with the help of the WebAIM WCAG 2 Checklist which makes WCAG 2 much more readable, and as can see, follows the form of WCAG 2, and of the VPAT. The checklist also highlights the new criteria in WCAG 2.1.
Since WCAG 2 is likely to form the basis of any accessibility conformance statement that you create, then this template is probably the closest you're going to get to just having to fill in the boxes.
If nothing else, completing the VPAT might be an eye-opener as to where you might want to make improvements to your product. In order to be able to say whether your product supports, partially supports, or does not support a WCAG criteria, then you're going to have to research the details that go in the third column of the VPAT anyway!
You can download the VPAT template from ITI
*I'm deliberately saying with the help of because WebAIMs checklist is simply a useful resource and they are very clear that the checklist should not be referenced in accessibility policies or policy adoption.