Why is the flight path from Taipei to Tianjin not a straight line?
This will be due to routing and the airways available. Looking at the Enroute Chart for the Taipei FIR, you will notice that there is no direct route northbound, but all routes have a north-east direction to remain clear of restricted area RCR8 (GND - FL370). 


(Source: http://eaip.caa.gov.tw)

The flight most likely, as I cannot find the flightplan, departed RCTP - Taipei via the DRAKE1A or DRAKE1B SID, leading to SULEM. Thereafter it continued westbound on the respective airways within China to then join another airway north.

This is consistent with the flightprofile tracked on flightware for EVA730 from RCTP to ZBTJ.


(Source: www.flightaware.com)