Hat Pattern not in the rounds?

I have a infant hat pattern that I want to knit using thick and thin yarn with size US 19 needles. The pattern does not specify what type of needles to use but I am assuming straight since it says to leave a long enough tail to sew up at the end. How would I shape it on straight needles?

This is the pattern:
Leave a length of yarn at the beginning of your cast on to use for sewing up at the end by measuring the length from finger tips to your elbow. Then make your first slip knot/loop for casting on

With 15mm needles
Cast on 19sts using the cable technique
row 1 knit row
row 2 purl row
row 3 knit row
row 4 purl row
row 5 knit row
row 6 purl row
start to shape crown
row 7 k1 [ sl1, k1, psso ] rpt to end (10sts on needle)
row 8 purl row
row 9 k1 [ sl1, k1, psso ] rpt to last st then k1 (6sts on needle)
row 10 cast off by purling through all 6 stitches at once) i.e. place your needle through all your stitches and make a purl stitch as normal).
Then thread the wool through the one stitch left on the needle, tightly and securely.

If you’re supposed to leave a long tail to sew up, that seems like it would be worked flat and not in the round. It doesn’t say to join, either and gives it in rows, not rounds; so just follow the pattern as is. Do you have a link to it or to a picture?