The NEC does not apply to a product like that.
Also 110.3(C) does not set any requirement for any type of product or equipment. It just sets the requirement for the organizations that listed equipment.
If local adoption is required before prosecuting a lack of compliance with a safety standard, like UL 962A standard for powered furniture, there are several ways to do this.
AHJ's may prefer other codes that cite adoption of safety standards for consumer products like household furniture, but there is also the argument for considering powered furniture an appliance.
422.6 Listing Required. All appliances operating at 50 volts or more shall be listed.
The scope of NEC 422.1 that "
covers electrical appliances used in any occupancy." is sufficiently broad that is does not exclude powered furniture as an appliance, per NEC 90.7 "specific items" requiring approval.
90.7 For specific items of equipment and materials referred to in this Code, examinations for safety made under standard conditions provide a basis for approval..
UL 962A
FURNITURE POWER DISTRIBUTION UNITS (IYNC)
Use And Installation
This category covers cord-and-plug-connected furniture power distribution units rated 250 V ac or less, 20 A ac or less, intended for indoor use when secured to a furnishing...
..The furniture power distribution unit may be provided with USB (Universal Serial Bus) charging outlets and LED lighting when three or more receptacle outlets are provided...
REQUIREMENTS
The basic standard used to investigate products in this category is UL 962A, ‘‘Furniture Power Distribution Units.’’...