For starters, Las Vegas Advisor.com isn't a gambling website. It's a Las Vegas site and bars, happy hours, etc. are part of Las Vegas. Also, while gambling and drinking are separate activities, in casinos they often overlap and they shouldn't necessarily have to be done exclusively of each other.
Taking the practical tack, the vast majority of gamblers will have greater control over themselves and their decisions if they don't drink while they play. It's well-known that alcohol flows free and freely in casinos because the result accrues positively to the house's bottom line. Do you want to make a plan for limiting losses and stick to it? Staying sober gives you the best chance of doing that. But many find the whole gambling experience to be more pleasurable when they're also getting the free drinks, so you have to decide for yourself.
When it comes to serious players, there's no doubt that most pros who play for profit shun drinking while they play. Note that we say most. Others can blend the two very smoothly and, in fact, incorporate drinking into their overall game plan. How? It has to do with being allowed to play in the first place. This applies in particular to blackjack, where winning is a two-part cocktail (if you will) of art and science.
Talking specifically about card counting, the science comes in the ability to count cards, recall strategy index numbers, and do the mental math necessary to play a winning game. A lot of players can master this part and if you could play blackjack in a vacuum, there would be a lot more winners. But blackjack is played in real-world conditions, where casino bosses are always looking for skilled players and will prohibit them from plying the science if they can.
This is where drinking while playing can come in very handy. Most bosses assume that serious card counters never drink on the game. So if you can drink and maintain your skill level, it goes a long way in the art of winning at blackjack, of which a big part is being able to get away with it.
Drinking usually has a part in the famous "big-player" scenario, where a player walks up to a game in the middle of a shoe and is signaled what to bet. The big player is often drinking while he plays, as it goes with his role of looking like a typical tourist.
Finally, gambling and drinking go hand-in-hand when talking about playing for alcohol comps. This happens in video poker, where rather than pay for a drink, you can play a few hands to get the drink comped and have a lower negative expected return than what you would pay to buy the drink retail.