In the first verse cited above, the word for "intoxicated" is sukara which is derived from the word "sugar" and means drunk or intoxicated. That verse doesn't mention the drink which makes one so. In the next verses cited, the word which is often translated as "wine" or "intoxicants" is al-khamr, which is related to the verb "to ferment." This word could be used to describe other intoxicants such as beer, although wine is the most common understanding of the word.
Muslims interpret these verses in total to forbid any intoxicating substance -- whether it be wine, beer, gin, whiskey, or whatever. The result is the same, and the Qur'an outlines that it is the intoxication, which makes one forgetful of God and prayer, which is harmful. Over the years, the list of intoxicating substances has come to include more modern street drugs and the like.
The Prophet Muhammad also instructed his followers, at the time, to avoid any intoxicating substances -- (paraphrased) "if it intoxicates in a large amount, it is forbidden even in a small amount." For this reason, most observant Muslims avoid alcohol in any form, even small amounts that are sometimes used in cooking.