Yes and no. Neural networks have a lot of nice properties like being easier to grasp, easier to parrallelize(?) and have better tools which i guess is because neural networks are applicable to more problems than SVM's because they are extensible.( see https://en.wikipedia.org/wiki/Recurrent_neural_network for example).

Either way SVM's still do what they do very nicely and in the field of "Human Activity Recognition" where i did my thesis neural networks are practically never used but SVM's pop up from time to time.

Apparently there are things such as structured SVM's and SVM networks, and models where they attach an SVM instead of the output neurons.

It isn't dead, and people are coming up with some pretty cool stuff, but NN seems to be where it is at right now.