Meat eating, illicit sex, intoxication, and gambling increase attachment to the body and the material world, so avoiding them helps our spiritual life.
Animals are also souls and to kill them unnecessarily is a great offense. By God's grace we can live perfectly well, and actually better, eating a vegetarian diet. If we're killing our brothers and sisters—the animals—and eating them, how can our Father be pleased?
Gambling is based on untruthfulness; trying to get something for nothing. Some examples are lotteries, slot machines, black jack, etc. One should labor honestly and accept what comes as God's mercy. Subtle examples of gambling include time-wasting activities like frivolous games and spectator sports. While these aren't considered grossly sinful, they don't help anyone's spiritual life, either.
Intoxication impedes clear thinking and makes it harder to remember God and do His will. Intoxicants are themselves material compounds; becoming attached to them binds us more to this material world.
Sex is meant for procreation of offspring, who are, in the ultimate issue, children of God, and thus should be educated to understand the human form of life is meant for developing our relationship with Him. Sex for that purpose is religious. Otherwise sex attaches us very deeply to our material bodies, the bodies of others, and this whole material world. Sex outside of marriage or outside of the purpose of having a child is considered illicit.