An intense emotional response could be responsible for some of the cases. But I don't think 700 kids had epileptic seizures. Flashing lights can synchronize brain cells so it gets cells into the synch mode. Normal consciousness depends on millions of neurons being synchronized and discharging electrical activity simultaneously. But sometimes that synchronization process gets out of control, resulting in a seizure.
Epilepsy is the failure to stop that process.
It occurs when synchronization gets out of hand. The United States uses NTSC video signals at 60 cycles per second, also known as 60 herz. That's faster than Europe and Japan, which both use a 50-herz cycle. Some who watched the Pokemon episode in question remarked on the oddly glowing red eyes of the characters. The red light may have some significance to the mysterious outbreak.