I thought, after looking at just a few of the words, that a Dotted Word might be one
made out of chemical element abbreviations.
Thus, e.g.,
ONLINE = O/N/Li/Ne and FRAMES = Fr/Am/Es.
Hence the hint saying that the puzzle
is "elementary".
However, this is demonstrably wrong; see below.
ONLINE = O/N/Li/Ne; DIGITAL fails because neither D nor Di exists.
HOWDY = H/O/W/Dy; HEY =He/Y.
URGES = U/Re/Ge/S; INSTINCTS fails because none of {Ct,T,Ts} exists.
NASAL = Na/S/Al; BARITONE fails because none of {It,T,To} exists.
FROG = Fr/Og; TOAD fails because neither T nor To exists.
POLAND = Po/La/Nd; UKRAINE = U/K/Ra/I/Ne.
WATER = W/At/Er; LUBRICATE = Lu/Br/I/Ca/Te.
FOLIO = F/O/Li/O; DOCUMENT fails because neither D nor Do exists.
COBRAS = C/O/Br/As; PYTHONS =P/Y/Th/O/N/S.
REBIND = Re/B/I/Nd; UNSEAL = U/N/Se/Al.
PRATTLER = Pr/At/Tl/Er, BABBLER fails because none of {Bl,L,Le} exists.
LUAU = Lu/Au; FIESTA =F/I/Es/Ta.
RECEPT = Re/Ce/Pt; RECEIVING fails because neither Ng nor G exists.
KNIFE = K/N/I/Fe; SPOON =S/Po/O/N.
FRAMES = Fr/Am/Es; BOXES =B/O/Xe/S.
LANDLADY = La/Nd/La/Dy; DUCHESS fails because neither D nor Du exists.
There are several counterexamples. But this seems to be close to working, and it's hard to believe it's coincidence. I suspect the intended answer is a variation on this theme and perhaps the variation explains why "Dotted Word" is the name.
It's very noticeable that
all the counterexamples are non-DWs that have decompositions, suggesting a rule of the form "a Dotted Word is one that has an 'elementary' decomposition such that ...". (This would also explain how it's possible that relatively few Dotted Words exist, even though a substantial fraction of all words have 'elementary' decompositions.)
A substantial fraction of the counterexamples
are non-DWs whose only decompositions involve noble gases, which (approximately) never form actual chemical compounds. But not all, and O/N/Li/Ne depends on Ne, so this is probably coincidence and in any case can be at most part of the answer.
A related conjecture would be
something along the lines of "a DW is a word with an 'elementary' decomposition that would be a possible chemical compound" or "... where each consecutive pair of elements can actually combine together somehow", but (1) that seems rather complicated and (2) S/Po/O/N seems like it fits any criterion of that sort at least as well as, say, O/N/Li/Ne does.
I notice that
all the Dotted Words have decompositions into at most four elements, and some of the Non-DWs with decompositions require more. (But note e.g. that Fr/Og uses only two elements; and that B/O/Xe/S requires only four but isn't a DW.) This is kinda suggestive of IP addresses, which is particularly interesting given Mike Q's comment to Glorfindel.
An obvious guess if it had worked in every case would be that "Dotted Word"
is just meant to hint at abbreviations, which are often indicated by trailing dots.
Or, more specifically,
conventionally one puts a dot at the end of an abbreviation exactly when its last letter is not the last letter of the thing abbreviated, so perhaps we could allow "Ra" but forbid "Rn" since it comes from Radon and wouldn't be dotted if we followed that convention for element abbreviations.
But clearly we need something smarter...