Irregardless, is a word in the sense that you will find it in the dictionary (in mine anyway) and people will, in fact, use it. However, the word is considered to be nonstandard because, as he points out, of its two negatives. In all fairness, it's a fairly new word (early 20th century) and is generally used to add emphasis, though it oftentimes just makes you sound foolish. It's a casual word, not formal as so many believe it to be, and it's considered a blunder by most.