No more than all Europeans are Greeks, or all Americans are Mexicans.
Asia is a vast continent with countless cultures, ethnicities, and languages. It would be ridiculous to call a Persian or Indian person Chinese, as they are not even ethnicially related.
(Non-Chinese) East Asian and South East Asian cultures are also quite different from one another. The reason for the similarities are due to China's influence on them. However, this does not make them any more Chinese than the influence of the Greeks and Romans on Britiain makes British people Greek or Italian.
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