It is burn out by now internally being it been on the that engine since 2000. But Norm said if it is very loud or if missing , I say it needs replacing is the muffler you indicated is a Lo-Tone version.
According to the parts manual, part no is 493288 lo-tone muffer. I am just in the process of checking if this is the one compatible with my mower as the picture on the website does not show this part that's connected to the mower. See attached phot.