The first and most common reason that you see wine served in casinos is for player's enjoyment. Above all else casino gambling is supposed to be entertainment and if a player is enjoying their time spent at the tables, they are more likely to spend more money. That is why you will see wine and other types of alcohol served. Nothing keeps one playing and in their seats better than to have a glass in their hand, it's the way many of us unwind and enjoy ourselves.
Another indirect reason that wines are served in the casino, and one that casinos will not admit to if directly asked, is that wine can impair players at the tables. By this we mean that players who regularly drink alcohol at the tables will not make the same types of decisions that a person that is not drinking will make. They will not be capable of using betting strategies as well or make the same types of decisions. In the end that increases the house edge on its players.
US casinos and many around the world will also serve wine to allow players to feel an air of sophistication when playing at the tables. For many, playing at the casino is about fantasy and feeling like a high roller. If someone is well dressed and sipping on Gaja Sito Moresco while playing blackjack, they will give off the appearance of being a high roller; they may even be treated better by the casino if they give off that air.
Finally, another reason you will see casinos serve wine is due to restaurants. Many casinos host a variety of restaurants, from buffets and cafeteria-style to fine dining and steakhouses. Nothing beats a great Cab when savoring a fine steak, a Riesling with your Thai or Chardonnay with most anything else. Offering a solid selection of wines gives customers the chance to enhance their dining experience, and increases the chance they will choose that establishment again the next time they want to dine out at the casino or spend their hard earned entertainment dollars.