If stations are not in sync, will that mean they cancel eachother out like with soundwaves and anti-sound?

No, it is worse than that.

If you think of two generators connected together in a power grid, they need to have the same frequency and the same phase. If one of the generators slows a little bit, it begins drawing current from the other. It in effect becomes a motor. Power flows as a proportion to the difference in phase angle.

All the other generators in that grid will drive the out-of-sync station like an electric motor at a faster or slower speed until it's synched up. In effect that's what's happening in the article. Unaccounted load is pulling other generators down, making the frequency unexpectedly low.

Perhaps they're not using just frequency to coordinate (solar/wind perhaps needs a sidechannel?), and someone on their grid in a politically unstable area is using power without reporting on the side-channel. Hence the frequency drops due to the unaccounted load.

An old joke says that the power plant starts rotating around the generator.

I imagine that they might cancel out, given limitless current flows between them. In practice, something would go bang long before that happened.

You're missing resistance losses, essentially. They would do no work (no real power component to the load impedance mismatch) but I^2 * R means the complex component would be entirely lost to transmission lines / coil windings.

But the effect is as you say: something goes bang.

Ah, this is very interesting. Thank you.