I realized there's a line in the code you modified that specifies all the unwanted tags. You should add the paragraph there.
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/* remove undwanted tags */
newSnippet = newSnippet.replace(/<(div|span|style|meta|link){1}.*?>/gi,'');
in the nicEditorInstance class, and change it to
/* remove undwanted tags */
newSnippet = newSnippet.replace(/<(div|p|span|style|meta|link){1}.*?>/gi,'');
Notice the "p" has been added. That will prevent nicEdit to wrap the paragraphs in
tags.