One of the more figurative definitions of "launch" is "put into operation" (see verb definition 2c-1). It can be used for any new enterprise, including ones related to transportation. Example:
Recently Uber launched their "Uber Eats" program, which allows you to order food from your favorite restaurant and have it delivered by an Uber driver.
Because "launch" is a rather dramatic term, it's generally used for the new release of some significant service. It's personal opinion whether simply designating women-only train carriages is significant enough.
It may depend on how big a deal Tokyo Metro is making of the new service. If they have extensively promoted the new service, then "launch" might make sense. Otherwise I agree the less dramatic "put into operation" sounds better.