Is this sentence a comma splice or dangler?

Noah Webster,author of the original Webster's Dictionary,believed that a dictionary should contain more than the definitions of words;therefore,he included their etymologies as well.

OR IS THE SENTENCE PROPERLY CONSTRUCTED?

There is nothing wrong with the sentence. It is not a spliced dangler. A semicolon is correctly used after "words", to separate independent clauses.

In modern usage, however, it would be preferable to omit the comma after "therefore". It is not needed to clarify the thought.