No Rummy (much like Poker) is considered a Game of Skill - as per a Supreme court ruling of 2015 does not fall under the ambit of gambling or betting - https://indianexpress.com/article/india/india-others/sc-clears-air-online-rummy-not-gambling/
Gambling is generally referred to as something purely reliant on chance or luck. But the SC clarified that Rummy isn't gambling, but requires a certain skillset to participate in and win and hence is not illegal. However, there is some ambiguity regarding the residents of the state of Orissa, Telangana, Nagaland, Andhra Pradesh, Sikkim and Assam. So most Rummy sites won't allow registrations from there.
As for proper betting sites -
@Ashk881 was pretty spot on in his analysis. I'd like to add that the whole ambiguity stems from the fact that there is literally "no rule" right now that explicitly prevents sites from operating in India and that all of these entities are registered offshore.
A lot of states amended their acts to prohibit betting, but none mentions "online betting".
Also, formation of an organization that enables betting is illegal in India. So all of these sites (Parimatch, Dafa, Betaway etc.) will take a license from an offshore country like Malta, Curacao, BVI etc. and then operate in India, while adhering to FEMA regulations.
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As for live gambling, I am sure you are aware of casinos like Deltin and Big Daddy in Goa. These casinos are permanently stationed in huge floating vessels on the Mandovi river - the whole vessel is a casino. To get to them, you take a feeder boat from the shores. Why? Because "casinos on land" is prohibited, casinos on water is not.

See? Ambiguity.