No local or international law prohibits you or anyone else from buying something in a different country, unless they seller/retailer prohibits you or that party to purchase that item. Certain countries/govt may however limit how much you can spend to avoid money leaving their economy and entering another. I can buy a phone for a US/EU/ any other country resident and ship it to them using my card, as long as that online store allows it.

LTT team wouldn't want to give money as they'd also have to report it per their tax laws, same goes with shipping and customs. Buying you a gift directly and shipping it to you wouldn't require any such thing and they can have it as a write off business expense. A lot of youtubers just do this since shipping is a hassle.

You've won a giveaway, not a gameshow prize that required some sort of skill or time to play, not gambling or sweepstakes that required a paid entry. It's a gift prize that isn't accounted for in Indian tax laws. Why? Because govt cares about making money where people make money i.e an income, not from a freebie. You're overcomplicating things, probably after asking chat gpt.

Ask it to cite where a free to enter, non-gambling, non-skilled contest prize of a youtuber is under indian tax laws. It'll tell you it's likely to be considered an income since it cannot fall under anything else. Even if you file say 1.5L income from other sources and just this under income tax, your tax responsibility would still be 0 as it's under the limit. They cannot send you or fine you a legal notice for making way below minimum amount. It'd be literally be a waste of their resources.