OP has separate tickets. He needs to check in with KE for the KE flight and then with DL (use the DL app and have the boarding pass printed at the airport if he doesn't have access to a printer in Hong Kong?) for the DL operated (and DL ticketed, so I assume it's not a codeshare) TPAC flight. KE does ground handling for DL at ICN, so checking in with DL there really means KE employees. However. Landside at ICN T2, there's a separate check in area for DL flights (versus KE's business class check in lounge for its own flights) where IIRC the staff wear DL uniforms.