Wait, actually, no, that won't work.
I just took a look at the pattern, and taking out all the YO's (and a decrease for each one) would leave you with all knit stitches on the following rows (the ones you'll have to change to remove the eyelet):
Row 4: k2, *yo, k3, sl1, k2tog, psso, k3, yo, k1; rep from *, end k2 instead of k1
Row 6: k2, *k1, yo, k2, sl1, k2tog, psso, k2, yo, k2; rep from *, end k3 instead of k2
Row 8: k2, *k2, yo, k1, sl1, k2tog, psso, k1, yo, k3; rep from *, end k4 instead of k3
Row 10: k2, *k3, yo, sl1, k2tog, psso, yo, k4; rep from *, end k5 instead of k4
sub-out the YO's for plain knit stitches, instead, try subbing-in another type of increase (make one, Kf&b, KLL/KRL) so you can still keep that zig-zag shaping but eliminate the holes.