Kenyans do buy products imported from Tanzania, it is more accurate to say that Kenyans are importing through Tanzania because of the higher taxes imposed on certain imports coming through Mombasa.
Calling Tanzania the “China of Kenya” is therefore just stupid. Kenyans don't import through China; they import from China products that are manufactured in China. In this case, they are importing through Tanzania, which is a completely different thing.
It's the same way Tanzanians import certain products through Kenya. The fact that a product passes through a country doesn't mean that the product originated from that country.