The intramolecular hydrogen bond in ortho-hydroxybenzoic acid between the $\ce{COO-}$ and the -$\ce{OH}$ groups forms a six membered ring.
Since this structure is very stable, the deprotonation of the acid is favoured and the compound is more acidic.
In the case of the para-isomer, there is hydrogen bonding between different molecules which is much less stable. Therefore it's acidity is lower than that in the ortho-isomer.
In the link you have provided, they explain the lower melting and boiling points of the ortho-isomer. That is again because of the hydrogen bonding, but it does not give an indication is the relative strength of the intra and intermolecular types.
To melt a compound, the intermolecular forces that pack them together must be eliminated. In the ortho-isomer, an intramolecular hydrogen bond is formed.
But this bond does not maintain the molecules together. When the molecules are separated, this hydrogen bond goes with each molecule in which it occurs.
So it does not matter if this bond is strong or weak. It has not to be broken.
On the other hand, in the para-isomer, the intermolecular hydrogen bonds maintain the different molecules together, so more energy is required to separate them.
The hydrogen bonds must be broken, and as a consequence, the melting point is higher.
This is the case in ortho- and para-hydroxybenzoic acid as well. The former has a melting point of $\pu{158 ^\circ C}$ and the latter has $\pu{215 ^\circ C}$.