Does NEC apply to temporary structures, container homes, trailers, houseboats, etc.?

It does apply to temporary buildings!

The NEC indeed does apply to wiring that is a permanent fixture inside a mobile structure, such as a mobile/manufactured home, RV, or office trailer. Which part of the NEC applies, though, depends on what you have.

Mobile and manufactured (distinct from modular homes and buildings, which are treated the same as site-built structures, save for a few notes found in Article 545) homes are governed by Article 550. This also applies to other types of temporary buildings such as office or worksite trailers and portable classrooms as per NEC 550.4(A):

(A) Mobile Home Not Intended as a Dwelling Unit. A mobile home not intended as a dwelling unit — for example, those equipped for sleeping purposes only, contractor’s on-site offices, construction job dormitories, mobile studio dressing rooms, banks, clinics, mobile stores, or intended for the display or demonstration of merchandise or machinery — shall not be required to meet the provisions of this article pertaining to the number or capacity of circuits required. It shall, however, meet all other applicable requirements of this article if provided with an electrical installation intended to be energized from a 120-volt or 120/240-volt ac power supply system. Where different voltage is required by either design or available power supply system, adjustment shall be made in accordance with other articles and sections for the voltage used.

RVs, pop-ups, towed campers, and other things not intended to be set on a permanent foundation (this category includes tiny-homes-on-wheels), however, are governed instead by Article 551, which largely parallels Article 550 save for RV-specific things, such as generator handling and combination AC/DC power systems. Note that 551.1 excludes circuits powered by the automotive DC system from Article 551's jurisdiction, though, so it's legal to use typical automotive wiring methods for 12VDC or 24VDC circuits powered from the trailer plug on a trailer camper or engine-alternator system on a RV. Also, 551.4 parallels 550.4 in that RVs used for non-dwelling purposes are covered by Article 551 save for the number and capacity of 120V circuits provided.

Houseboats though, are a more interesting case...

When you get to things that float, though, the situation becomes murkier. The NEC governs non-navigable, permanently moored floating buildings in Article 553, as long as they have a connection to an off-premises supply system (such as a utility, or some sort of shore-based "microgrid"). However, NEC 553.2 excludes a completely self-powered ("off grid") floating building from the definition of "floating building" used in NEC 553:

553.2 Definition.

Floating Building. A building unit, as defined in Article 100, that floats on water, is moored in a permanent location, and has a premises wiring system served through connection by permanent wiring to an electrical supply system not located on the premises.

Furthermore, if what you are talking about is actually a navigable vessel that can reasonably be unmoored and towed or piloted around whatever body of water it sits on, the NEC's application becomes very murky indeed. This is because while the NEC itself excludes watercraft, aside from Article 553 floating buildings, from its jurisdiction in 90.2(B):

(B) Not Covered. This Code does not cover the following:

(1) Installations in ships, watercraft other than floating buildings, railway rolling stock, aircraft, or automotive vehicles other than mobile homes and recreational vehicles

Informational Note: Although the scope of this Code indicates that the Code does not cover installations in ships, portions of this Code are incorporated by reference into Title 46, Code of Federal Regulations, Parts 110–113.

the Coast Guard electrical engineering regulations in 46 CFR Subchapter J include parts of the NEC by reference, as mentioned in the FPN above. However, 46 CFR Subchapter J itself does not apply to uninspected vessels governed by 46 CFR Subchapter C, and houseboats, by and large, are considered uninspected vessels, as they do not operate in any sort of trade service. The main document that fills this gap is ABYC standard E-11, but this is a voluntary construction standard; 33 CFR Subpart I captures the most important requirements, but only applies to boats powered by inboard or inboard-outboard gasoline engines, not purely outboard gasoline engines, purely sail-powered vessels, or diesel-powered boats.