As we explain in the course notes, the colloquial pattern with eisiau (and also with angen) is an exceptional one in Welsh.
Words such as hoffi, bwyta, cerdded, etc are verb-nouns, and in that form they need yn to make a link from dw i, dych chi, etc and so make the usual, 'long-form' pattern of a verb in colloquial Welsh..
eisiau is a noun meaning 'a want', not a verb-noun at all. You may occasionally see, in more formal Welsh, a pattern such as Dw i ag eisiau xxx for 'I want xxx', where ag means 'with' - literally 'I am with a want of xxx'. Perhaps through frequent use, the ag has been dropped in day-to-day Welsh.