Rig-

"Joe the Plumber doesn not need a license to work as a plumber for somebody else in the state of Ohio."

That conclusion does not appear to be supported by the sections of state law that you posted, which doesn't necessarily surprise me. In fact, please review Section C:

(C) "Licensed trade" means a trade performed by a heating, ventilating, and air conditioning contractor, a refrigeration contractor, an electrical contractor, a plumbing contractor, or a hydronics contractor.

"Plumbing" is identified as a "licensed trade" and therefore anyone who practices it for "compensation" would need to acquire a license.

Charley Noble, who knows better than to do his own plumbing