Yes G-Sync only works with NVIDIA cards. As is the other way around. FreeSync only works with AMD cards for now. Difference is that NVIDIA could support FreeSync if the wanted.
Well, to be accurate, Nvidia cannot ever support FreeSync, as that is an AMD-only feature of their GPUs. FreeSync is a GPU/driver feature, built on a standard. FreeSync relies on a monitor that supports VESA DisplayPort Adaptive Sync.
As it's an optional part of the VESA DisplayPort standard, any GPU manufacturer
could support DisplayPort Adaptive Sync and give that feature whatever name they wish. It's just at the moment there is only one company doing so and that company has called their feature FreeSync.
Nvidia have said they have no plans to support DisplayPort Adaptive Sync at the current time, which is completely unsurprising as they've invested in G-Sync.
I expect Intel are quietly looking into DisplayPort Adaptive Sync for their Iris GPUs (although imo it's not really that important for low end GPUs like Intel's and they probably already support the functionality as a result of laptops and eDP). Prepare for iSync, or whatever Intel decide to call their feature.