Maaaaybe. I tend to think that symbolic reasoning is a learning tool, rather than a goalpost for general intelligence. For example, we use symbolic reasoning quite extensively when learning to read a new language, but once fluent can rely on something closer to raw processing - no more reading and sounding out character sequences. Similarly with chess - eventually we have good mnemonics for what make good plays, and can play blitz reasonably well.
And - let's be real - a lot of human symbolic reasoning actually happens outside of the brain, on paper or computer screens. We painstakingly learn relatively simple transformations and feedback loops for manipulating this external memory, and then bootstrap it into short-term reaction via lots of practice.
I tend to think that the problems are:
a) Tightly defined / domain-specific loss functions. If all I ever do is ask you to identify pictures of bananas, you'll never get around to writing the great american novel. And we don't know how to train the kinds of adaptive or free form loss functions that would get us away from these domain-specific losses.
b) Similarly, I have a soft-spot for the view that a mind is only as good as its set of inputs. We currently mostly build models that are only receptive (image, sound) or generative. Reinforcement learning is getting progress on feedback loops, but I have the sense that there's still a long way to go.
c) I have the feeling that there's still a long way to go in understanding how to deal with time...
d) As great as LSTMs are, there still seems to be some shortcoming in how to incorporate memory into networks. LSTMs seem to give a decent approximation of short-term memory, but still seems far from great. This might be the key to symbolic reasoning, though.
Writing all that down, I gotta say I agree fundamentally with the DeepMind research priorities on reinforcement learning and multi-modal models.