This is a typically ridiculous Cassidy claim. Booze is a long-established word in English, both as a verb and as a noun. Scholars have quite rightly identified that this word is linked to the Dutch word busen, which meant to drink to excess.
Cassidy disagrees. On the basis of his vast knowledge of the Irish language (!) he believes that this word derives from an Irish word beathuis. Now, you will search in vain for this word in the dictionary. Beathuis is not a real word. Even if it were real, it wouldn’t sound much like booze. It would be pronounced as bahish.
Where did Cassidy get this word? Well, there is a word beathuisce (life-water) in the dictionaries. It is a variant of the vastly more common uisce beatha (water of life) which is the origin of English whisk(e)y. This variant seems to be found mostly in songs and poems and is probably used in these contexts for reasons of metre, because it has 3 syllables rather than 4. It is pronounced bahishka. So what about the inconvenient –ka at the end? After all, nobody talks about boozeka in English! According to Cassidy, beathuisce was shortened to beathuis. He gives no evidence of this or reason for it, and it seems about as likely as someone in English contracting the word water to wart.
So, to recap, there is a perfectly good derivation from Dutch which fits the facts, sounds right and has the right meaning. And there is a completely improbable candidate which doesn’t sound like booze and which was made up by Cassidy by mutilating a rare variant word beathuisce, the ‘word’ beathuis.
Which is correct? I’ll leave you to make up your own mind on that one!