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.

From what I understand, the TPP is closer to the KMT than to the DPP. They have refused to form a coalition, but they abstained so that the KMT could get the Speaker and Deputy Speaker posts. Also the DPP won the presidency, so the legislature and executive are now led by different parties.