The thumb gusset is, like other’s said, all those increases between the purl stitches.
So, if I’m reading you correctly, you’ve reapeated rows 7 and 8, purled on row 9, and the line giving you trouble is:
Next Row: Follow S1, K1 pattern to and including first p st. Work in pattern across next 8 sts of thumb. Turn. CO 1 st and p across - 9 sts. Turn. CO 1 st - 10 sts.
Work in pattern on these 10 sts to 2 rows less than required thumb length.
K2tog across row.
P2tog on next row.
Yes, that is knitting the thumb, and no, you don’t need to move anything to stitch holders, because you using short rows to create the thumb.
So, on the right side, you knit across one side of the hand in pattern, then you’ll come to the first out of pattern purl stitch (all of your increases for the gusset start here). Now work those increased stitches, 8 of them, in pattern, but not the purl stitch that comes at the other side. Turn your work. You will still have all the “hand” stitches still un-done, and that’s ok, this is a “short row” because you are turning before the end of the row. Cast on one stitch, then knit only those 8 again - those 8 plus the cast on gives you total of 9 thumb stitches between the purled stitches. Cast on again, to give you 10, then just knit only those 10 stitches - the 10 that are now between the purled stitches until it is almost long enough to cover your thumb, then do the 2 decrease rows.
After that the instructions tell you how to sew the thumb so your working yarm ends up right back where you need it to finish the hand part of the mitten