Differential privacy is a formal guarantee of an algorithm. Roughly, given algorithm A that takes input database X, we say A is differentially private if m, for any X' differing in at most one row from X, the output distributions of A(X) and A(X') are similar. So to say an algorithm is differentially private you need to prove a claim like this.

It's hard to compare to this paper, because this paper's privacy claims appear to be heuristic, not formal. This isn't necessarily bad, since existing approaches for constructing synthetic data in a differentially private way is still not very practical. But heuristics do necessarily lack provable privacy guarantees, so there's no proof that something very bad privacy-wise can't happen with sufficiently clever processing of the synthetic data.

To add to this answer: the methods outlined in the paper allow for perfect reconstruction of the underlying data in many cases, as the simulation of data is simply sampling from fitted distributions.