Are attacks on AES more efficient now (due to the new paper published at CHES2016??)
Practically not, for two reasons:


the method described mostly speeds up AES computation with repeated use of the same key, rather than AES computation with repeated use of the same data, which is what a brute-force attacker does for key search, and what a side-channel attacker does to narrow a guess (there are other attacks, like detecting collisions in the CBC ciphertext, but a faster AES engine does not significantly help these).
even a speed up by a factor of 4 (more than claimed by the paper) would not qualitatively change the fact that AES key search, or other known AES attacks (excluding attacks on a particular implementation), are hopeless (when a single key is targeted, or when AES-192 or better is used); the technique in the paper reduces the security of AES-128 to 126 bits instead of 128, akin to reducing distance to notable nearby galaxies (excluding the Milky Way where we stand) to that of the Carina Dwarf instead of that to Andromeda.


Note: I have excluded side channel attacks against AES implementations using the technique described, but not use of the technique described to attack other implementations.