Would 'is this the Chinese language' be a more proper translation?
Nope, that would mean "Onko tämä kiinan kieli?"
why is "kiina" in the partitive here? is text in a language always partitive, as opposed to the language itself?
Yes, and also speech. It's some Chinese as opposed to all of the entire Chinese language, so it's partial and therefore partitive case is required.
Does the expression "this is chinese to me" also exist in finnish?
Chinese is replaced by Hebrew (heprea) in that expression.
In german it's spanish
Could "kiinaa" also be used here to refer to food? Based on context of the situation I was thinking this could also mean "Is this some Chinese food?"
No. "Kiinaa" is a language. Chinese food could be shortened to "kiinalaista" if it's clear from the context that you're talking about food.