I'm not sure a question like this has a black and white "legal" answer. But my experience and advice would be that you should make sure you are understanding how those previous challenges and answers would apply to the new issue, but you don't necessarily need to reread the text in order to make a siyum on the tractate.
When I have been in shiurim (including that very pasage in beitzah), I have never seen anyone literally reread the previous back and forth verbatim. And I have never heard of a source saying you must do so in order to make a siyum. You are not "skipping" if you just read what's on the page and don't re-read the text above. The same way that you aren't "skipping" when the Gemara only cites part of a verse or part of a mishnah or makes a passing reference to a story recounted elsewhere or says "etc." None of these are a coded way of saying "you must stop and look up the text there as if it were written here if you want to consider yourself as having learned this page."
In concrete terms, as applied to your gemara, you hopefully understand how Rabbah understood the mishnah (that it was a rabbinic decree for a specific reason), Abayei's challenges showing why he thinks there is no such rabbinic decree, and the gemara's answers. What the gemara is saying here (and I assume you understand) is that Rav Yosef has given a different reason for a basically identical decree, so you should be able to understand why those challenges and answers apply just as well to Rav Yosef's theory (because Rav Yosef and Rabbah are proposing basically the same decree just for different reasons).