Under Cabinet exposed NM/Romex
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Comments in parens are my rewording.

334.10 Uses Permitted
Type NM ('Romex')....shall be permitted in 1 and 2 family dwellings, and multifamily dwellings of types III, IV and V construction
(and other buildings, but must be concealed)

A "For both exposed and concealed work in normally dry locations" (except buildings other than 1 and 2 family dwellings, and multifamily dwellings of types III, IV and V construction.)

334.15 Exposed Work

A To Follow Surface

Cable shall closely follow the surface of the building finish or of running boards

B Protection from Physical Damage

..."where necessary" (describes which types are acceptable)

Which means if the electrical inspector thinks the wire is exposed to physical damage.

So bottom line, this is "exposed" but 
"closely follow(s) the surface of the building finish" and doesn't seem "exposed" to significant physical damage, unless the inspector thinks so so it is code compliant if not elegant.  

It seems unlikely the residents will poke sharp objects up there.

Article 320 is 'Armored Cable' Type AC, which says,
"320.10...shall be permitted...in both exposed and concealed installations"

"320.12 ...Type AC cable shall **not be used...where subject to physical damage**"

In this situation, AC is allowed exactly the same way as NM in a 1-2 family house, which I'm assuming is the situation..

For the LED jumpers, you'd have to look at what kind of wire they are.