It is not “your HTML”, it’s HTML 4.01 from 1999, when XHTML 1.0 is from 2000. The common is the origins of validations that comes from W3 validator (1).
Current websites that are valid XHTML 1.0 Strict (or Transitional)
Back to tirreno website, it is a pure transitional HTML 4.01 without JS or CSS, thus more or less same challenges to make it W3 valid (2) in our days. Have a look.
but what you are describing is XHTML 1.0, not XHTML in general.
HTML5 has its XHTML variant too, sometimes called XHTML 5.