The issue of online gambling as per Indian laws still remains a grey area which is yet to be adjudicated by courts of India. However, inferences can be drawn from the orders passed by the Court.
The situation with online betting in India is not 100% clear. Officially, betting and gambling are illegal in India. However, no laws specifically make online betting illegal. The Public Gambling Act, 1867 is a central legislation that prohibits all games of chance except lotteries and games of skill.
Online Gambling laws in India prohibit betting or wagering and any act which is intended to aid or facilitate the same. Gambling being a State subject differ from state to state.
There are two types of games: a game that requires skills to play and a game that doesn’t require any skill to play. Betting or gambling on games that don’t require any skills to play i.e. games that are purely based on luck is illegal in India. But, games that require a certain set of skills to play are allowed in terms of betting
After going through your query, in my opinion, horse race betting is legal in Tamil Nadu according to the famous case Dr. K.R. Lakshmanan vs State Of Tamil Nadu. Supreme Court held that horse racing is a game that requires skill.
I hope this helps.