Can molecule have just h-bonds between its parts
There are some grey areas in the normal usage of the word 'molecule'
The normal usage of the term molecule is accurately described by your quote from the Khan Academy. The majority of molecules chemists talk about are groups of atoms joined with covalent bonds. But, like many things in chemistry, there are some grey areas and the normal usage gets bent a little.
One of the major areas where the terminology gets fuzzy is in polymers. While on a strict interpretation of the normal definition a single polymer strand (be it DNA or a single strand of polyethylene) is a molecule the terminology is not particularly helpful as the key things that matter in bulk polymer properties are not easily reduced to the properties of individual 'molecules' so the very idea of molecules is less relevant. In polyethylene (a very simple polymer) there will not be a mix of identical molecules but, rather, a wide range of very similar molecules (even for linear polyethylene there will be a wide range of chain lengths (say from 1,000 to 10,000 carbons). So polymer chemists tend not to talk about molecules much.
DNA is a polymer but, by its nature, one where the structure of a given strand is constant (and can be precisely replicated). We do tend to say DNA molecule at least in casual conversation despite the fact that the two strands are connected only by hydrogen bonds. But there are good reasons why this is not an abuse of the normal definition of molecule. One is that many hydrogen bonds along a polymeric chain add up to a strong overall bond even though the individual bonds are merely hydrogen bonds. But the relative weakness of each bond is a key part of the process of replicating DNA as the two strands can be easily unzipped by the machinery in the cell nucleus. You could argue that a DNA strand consists of two molecules using the normal definition but this doesn't help much and, in normal discussion, we talk about both a DNA molecule with two hydrogen-bonded strands and a DNA strand as a molecule. This mild abuse of a strict definition of &quot;molecule&quot; doesn't matter much as it doesn't interfere with any understanding of how DNA works.
Mostly, though, chemists don't consider hydrogen-bonded units as &quot;molecules&quot; even when the bonds have significant effects on the bulk properties of the substance. The physical properties of, for example, acetic acid are heavily influenced by hydrogen bonding. In solution molecules often form pairs (joined by two hydrogen bonds) and this leads to a big elevation in their expected boiling point compared to a similar hypothetical molecule of the same size that couldn't do hydrogen bonds. But there is no benefit in describing this a &quot;molecule&quot; and nobody does this.
But the main point is that many properties in chemistry have an almost continuous range with no clear point where a black and white distinction can be made. The definition of what counts as a molecule is like this. Describing hydrogen bonded DNA as a molecule isn't a terrible use of the terminology; describing an acetic acid hydrogen-bonded pair as a molecule probably is. The term molecule can be useful in some circumstances but not others. The utility of the term is what matters not a simple black or white definition.