In this context "a mosque" means a room set aside for prayer.

All hospitals these days, and lots of other public buildings have rooms set aside for prayer. Christians, Moslems, Buddhists, Hindus, people without any religion, anything you like - they can all pray or meditate or whatever there. That's what rooms set aside for prayer are for.

I would think it a very reasonable idea that the massive commercial offices that are being built on Ground Zero should include a multi-faith prayer room alongside the money-making facilities. If it doesn't that might be reasonable enough grounds for people to make a fuss about the omission. In contrast to this very nasty stuff that has been drummed up by hatemongers.