No, this Southbend 1073498 Off/Low/High Burner Valve Knob is not the one you'll want for your 1363CHT gas range. There are a couple options for your unit. Southbend part #1160534 is a black top section knob that's marked "on/off" and part #1166011 is a black knob marked "off/high/low".
I've included both knobs below for your convenience.