It is certainly an enviromental disaster, but the rumours are clearly OTT.
I doubt that a nuclear weapon will be used to seal the well, and IF this dramatic option IS decided on, I doubt that any evacuation would be needed, a small nuke, detonated in a deep hole submerged in deep water is unlikely to have much effect on land. The area would probably be closed to shipping.

The main concern is the damage to wildlife and fisheries which is very severe, the direct effects on human health are probably limited to those directly exposed, for example by assisting with the clean up.

Small numbers may need to be evacuated from communities right on the affected coastline.

As for the affected area extending 200 miles inland, that depends on how you define affected. But I would not expect any significant effect that far away.