Why is does the protocol of Ding et al. produce biased bits and does it relate to passive security?
The usual definition of (passive) security for key exchange requires the agreed-upon key to be indistinguishable from uniformly random. That's not the case for DXL14 because the bits of the key are biased, not uniform. You can check that yourself if you implement the DXL 14 algorithm in (for example) SageMath. It shows that bits are biased and not uniform. 

Now, you may wonder: is it because it uses Polynomial instead of Vector of polynomials, because of limited domain of $\mathit{Sig}$  function (i.e. $E= {-\lfloor {\frac {q}{4}}\rfloor ,...,\lfloor {\frac {q}{4}}\rceil \}}$), or if there’s some other reason?

Well, it's simply because any deterministic map from $\mathbb{Z}_q$ to 0,1 must be biased when $q$ is odd.