I don’t think any of these examples were what Illyes meant when he talked about HTML structure. I believe he was referencing the common arguments of heading nesting, bold tags, etc. TL;DR ...

Thus, if the site uses invalid HTML markup (e.g. multiple H1 tags, or one and the same headings on each page), the worst what must happen is that Google will just disregard the overall structure ...

H1 – H6 elements “briefly describe the topic of the section they introduce“.They form a page HTML semantic structure that can “be used by user agents, for example, to construct a table of ...

Lower degree headings should be contained within headings of the next highest degree (i.e., one should not skip heading levels, such as from a Heading 2 to a Heading 4, going down the page or document ...