I'm an outsider looking in who's not particularly familiar with the structure of Taiwan's government, but apparently a coalition is possible but not required. The executive is appointed by the president, which is elected separately and still held by the DPP. The Kuomintang seemingly failed to negotiate a coalition with the third largest party, so now nobody has a majority in the legislature. Presumably anyone that proposes legislation will just need to get the agreement of one of the other parties to get anything done.