Yes, if you received more than $600, you are required to file a MO Non-Resident income tax return. MO does tax unemployment benefits.
You should complete your MO Non-Resident income tax return before your KS resident tax return to insure proper tax credits.
Sources: http://dor.mo.gov/personal/nonresident/ and
https://molabor.uservoice.com/knowledgebase/articles/282975-are-my-benefits-taxable
