No they mean increase. Rents are high and it is causing problems for retail workers who have to commute 2h to get to work because of living costs in the city.

If you tax vacancy then you're discouraging vacancy which would encourage non-vacancy (decreasing vacancies). The Empty Home (Vacancy) tax is to encourage owners to either sell their vacant property (which would increase supply and lower prices) or lower rents on their vacant properties to find tenants and fill their home. The goal is to decrease vacant (empty) homes and lower housing costs for people that desire to live there.

I think by "vacancies" they mean "vacant homes on the market", versus "vacant homes the owner is sitting on." A tax would encourage vacant homes to be put on the market.