You are correct in that you have a second oil drain plug. Again, this is VERY common on multi-application engines. Some times it works better on one side and other times, they use the opposite side.
The plug that you received, appears to be for a horizontal crankshaft engine. They use the integral oil plug/ dip stick on the smaller 3-8 horse Briggs and Tecumseh series . Again, similar to your engine and depending on the application, it varies as to which side the dipstick and fill hole will be found. Many times they plug the unused port with the plug that you ordered. It is not intended to be used on the engine that you have in your tractor.