i guess its because as vice mayor, one is in charge of the city council which enacts local ordinances. as for the executive, it does say "as chief executive" so being cabinet member would not qualify (in fact nothing short of being the head will - ie. President, Mayor, Governor). as for the dates, i think its 1988-1998 meydo blurred lang yung image. the source is "Riyadh Travelers" which is either a travel agency, some foreign company or a group of OFW. either way, it doesn't seem like its based on actual statistics, rather just a compilation of facts that the group knows about the candidates
with regards to government experience, all the candidates (perhaps except Grace Poe) has had more than 10 years experience with Philippine government. but then again government experience isn't the only barometer for choosing