To the extent that computations are feasible, yes. There was a pretty big paper like a decade ago proposing a fully homomorphic system. It was pretty much impractical, running like a million times slower than native instructions. I assume without reading that this post's paper reduces that multiplier to hundreds of thousands.
edit: reading the abstract, it looks like they don't have a faster fully homomorphic system, just some better results in the partial homomorphic domains.
Theorem 1 fails to specify what it means to "attack" the cryptosystem; it seems to deal only with complete plaintext recovery. It is possible that an attack can only recover a single bit of the plaintext, something which is not handled by the proof.
Definition 1 is not really a definition; in particular it would not be useful in a proof or logical argument. Likewise with Definition 2.
The authors claim that chosen plaintext attacks are not relevant; then they claim in Theorem 3 that their system is secure against CPA. Over and over in this paper the authors refer to the need to be CPA secure when the plaintext has "insufficient entropy" so it is hard to understand why they would claim CPA security is irrelevant.
The vector version of their scheme appears to be a lattice problem, but the authors do not discuss lattice attacks that might be used against their scheme. The authors state that it is "clear" that the security of the vector version follows from the same arguments used for the integer version.
In the "FHE" section the authors do not actually construct an FHE scheme; instead they have constructed some kind of garbled circuit scheme that uses the encryption schemes proposed in the paper. No proof of security is given for that garbling scheme.
For what it's worth, this is more or less what I would have written if I had to review this for a conference and I would give this paper a "strong reject" score.
edit: reading the abstract, it looks like they don't have a faster fully homomorphic system, just some better results in the partial homomorphic domains.