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This is a meaningless question. First, you count medieval "Arab" contribution as "non-western", while it is well-known that Arab mathematics comes from the Greek and Mesopotamian sources. Arabs did not invent mathematics themselves but developed Greek and Mesopotamian mathematics. Is Mesopotamian mathematics "western"?

Really, mathematics cannot be separated into "western" and "non-western" until 17 century. Greek mathematics was influenced by Mesopotamian tradition. Muslim peoples inherited Greek and Mesopotamian mathematics. Indians too, to some extent. Then Europeans of 16 century learned a lot from Muslim (and Indian) mathematics, including many achievements of the Greeks. Much of trigonometry, and positional number system is of non-European origin.

And why is Greek mathematics WESTERN? Greece is in Eastern Europe, by the way, and most significant Greek mathematicians worked in Africa, namely in Alexandria. And Western European civilization is very different from the Greek one. Yes, we inherited Greek mathematics but so also the "Arabs" did. (I use quotation marks because many medieval mathematicians were not Arabs but Iranians and people from Middle Asia).

It is indeed very hard to tell which tradition never experienced Greek influence. (Perhaps American-Indian is the only clear case).

Second, you mention Chinese reminder theorem and African independent discovery of Fibonacci numbers. Can we really say that these independent discoveries CONTRIBUTED anything to Western Mathematics? Did Western mathematicians really learn them from Africans and Chinese? No. There is a difference between "discover independently" and "contribute".

Let me give another clear example which is well documented. In 18th century Japanese mathematician Seki Takakazu developed the theory of determinants. Few decades earlier than his European counterparts. But did European mathematicians learn anything about determinants from him? Did Japanese mathematicians of 20th century study determinants from his work? No, they studied them from "western" sources.

After the Meiji revolution, the door for cultural exchange was wide open, Japanese students learned "western mathematics" very quickly and started to contribute to it on the highest level, since approximately 1900. But they learned it from European sources, not from native Japanese sources.

Did European mathematicians really learn anything new from pre-19 century Japanese mathematics? I strongly doubt it. There was a high quality mathematics in Japan before 19th century, but it did not contribute to modern mathematics.

I dare to claim that none of the famous mathematicians who made a substantial contribution to modern mathematics did this by developing any "non-western" tradition, no mater where this mathematician comes from. Even when some of them claim the contrary. One cannot contribute anything essential to modern mathematics without being educated in this "western tradition".