Why is ortho-hydroxybenzoic acid more acidic than its para-isomer?
I don't think that in the first link it is stated that the intermolecular $\ce{H}$-bonding is stronger than the intramolecular one. On the contrary, the accepted answer starts as:

"I don't think there is much of a difference between the strengths of intramolecular or intermolecular hydrogen bonds."  With which I agree. 

In that post they discuss the effect of intermolecular and intramolecular $\ce{H}$-bonding on the melting and boiling points of the compounds. 

The answer by @AllYouCanEat86 that follows in the same post I think is more relevant to your question.

Therefore in our case there are intermolecular $\ce{H}$-bonds in p-hydroxybenzoic acid but they don't last for long due to the thermal motion and higher degrees of freedom of the $\ce{COO-}$ and $\ce{OH}$ groups. In contrast, in the ortho-isomer the $\ce{COO-}$ and $\ce{OH}$ groups are locked in close proximity due to the aromatic ring and therefore are forced to maintain the $\ce{H}$-bond for much longer. This could be thought as an equivalent to the chelation effect in metal complexes. Lastly, one could also argue that in the case of o-hydroxybenzoinc acid, there is both the option of intermolecular and intramolecular $\ce{H}$-bonding compared to the para where there is only intermolecular $\ce{H}$-bonding.