Pyjamas, guru, khaki, avatar, bandana, jodhpurs, and shampoo are but a few of the many words drawn from Hindi and Sanskrit.
Urushiol, kudzu, futon, and karate from Japanese.
Orangutan, bamboo, cassowary, paddy, ramie, rattan, gong, and camphor from Indonesian (and related languages).
Ammonia, banana, bongo, cola, dengue, ebony, and gnu are of African origin (numerous languages).
Algebra, algorithm, alchemy, and alcohol all come from Arabic ('al' is the definite article in Arabic). So too do numerous terms for textiles: chiffon, gabardine, satin, tafetta, and wadding. Tahini, tuna, tamarind, talc, tangerine, and talisman as well.
All these use a non-Latin script, in some cases no script at all.
Fair point as I'd chosen to use Hindi (culture) rather than India (geographic region), though of course India itself derives from Hindi (the word).
A fuller set of candidate languages, from Wikipedia: Hindi, Urdu, Kannada, Malayalam, Sanskrit, Tamil, Teluga, Bengali, Assamese, Bengali, and Marathi.
I'm sure someone will pitch in with specific sub-dialects as well shortly.
I'd reported languages based on Wikipedia's citing. That's publicly-editable, and if you have sourced references the links I'd provided can be updated.
Urushiol, kudzu, futon, and karate from Japanese.
Orangutan, bamboo, cassowary, paddy, ramie, rattan, gong, and camphor from Indonesian (and related languages).
Ammonia, banana, bongo, cola, dengue, ebony, and gnu are of African origin (numerous languages).
Algebra, algorithm, alchemy, and alcohol all come from Arabic ('al' is the definite article in Arabic). So too do numerous terms for textiles: chiffon, gabardine, satin, tafetta, and wadding. Tahini, tuna, tamarind, talc, tangerine, and talisman as well.
All these use a non-Latin script, in some cases no script at all.