The target of this sketch is, of course, Shakespeare's Antony and Cleopatra. Some of the humour is a bit dated, some of it is incomprehensible outside of Britain, but some of it is pure genius - particularly the Egyptian dancing and the reference to 'beauty like what I have got', delivered in grand Shakespearean style.
None of the sketch is really engaging with the ancient world itself, other than indirectly through stories made popular by Shakespeare, like Cleopatra and the asp. I always find it interesting to see receptions of the ancient world that are really receptions of Shakespeare, since it boils ancient history down to a few repeated components, which become the most famous incidents and characters from the ancient world. This happens particularly often in material from the 1960s and 1970s, presumably because after 1964's Fall of the Roman Empire, there were no major Hollywood epics set in the Classical world (there were other films - art films like Pasolini's Medea, or Sebastiane, or Fellini Satyricon, but not the big popular epics). These days, audiences tend to engage with the Classical world through well known films like Gladiator or 300, but in older comedy, Shakespeare is often the focus (and Cleopatra, of course) - at least until 1976, when I, Claudius came along.
Anyway, this sketch is deservedly famous, partly just because it's funny seeing an actress so well known for serious roles and for playing powerful Queens (Elizabeth I in Elizabeth R) speaking Ernie's lines. I love the bright purple feather-duster-style fan and the way Cleopatra dangles grapes over Eric's face, undercutting the classic symbols of decadence (so cliched now I can never take them seriously, even in otherwise perfectly serious scenes, like some of Maecenas' scenes in Rome). I also like the gag with Eric's shoes, which is one of those jokes you watch as a child and think nothing of, then watch again as an adult and suddenly realise what the joke was - with appropriate horrified reaction at the idea these idols of your childhood knew what sex was (don't get me started on the asp bit). Clips from this sketch quite often appear on comedy compilation and celebration shows, but thank you to whoever uploaded the whole thing to YouTube - it's great to see it in full!