Yes they are important. When you pull the soft top tight via the clamps the straps put tension on the rear of the soft top. Without the strap there is nothing holding the rear portion of the soft top in the air and your soft top will collapse. Whoever sold you that soft top frame should refund your money.
Or you can figure out another way to secure some form of strap to the soft top hardware. The original strap is riveted to the tubes. Should be easy to figure out. Or sew the thing back together.