I disagree with explanation of Andersen, but there are few important points correctly formulated.
main one is
ticket price segmentation issue
has better comfort railcars and that combined with the higher speed justifies a higher price tag than on train
is incomplete, because in fact higher comfort cars separately and higher speed separately increase price less significantly, so for having them in combination passenger overpay more, than the sum, that's the key problem of NE trains now.
justifies a higher price
is more correct regarding NE 111/112 and 113/115. Those train helps to overcome distance from Lviv to Kharkiv in one night.
So they are popular, despite passengers overpay for speed and for better car in total more than usually, but it's justifie because save you too much time (with non-NE speed you definitely need spend some of busines hours for riding even if you also ride all night).
In case of 129/130 in don't work. Especially taking to account, that 129/130 goes roundabout way via Vinnytsia - Khmelnytsky - Ternopil, what is especially stupid for NE - because passengers from Vinnytsia - Khmelnytsky - Ternopil not so strongly tend to overpay for higher speed than passengers from/to Kyiv, also train passes those 3 cities in inconvenient hour, so by its speed 129/130 saves non-business hours.
But due to going via Vinnytsia - Khmelnytsky - Ternopil train saves less time for passengers to/from Kyiv too, because wins less than possible between Kyiv and Lviv. So 129/130 is total fail in general.
But instead of canceling or correcting of 129/130 - UZ decided to find passengers for it in other way.
Understanding this is very important for appearance of 213/214.
So my personal opinion - the only motivation of UZ in this case was increase the demand for 129/130 which is obviously not satisfactory enough now.
So they didn't want to acknowledge drawbacks of 129/130, but decided сoerce passengers to choice of 129/130 by small increasing the deficit of places on usual trains from Uzhhorod to Kyiv. So on days when 129/130 is in operation - 13/14 don't reach Uzhhorod now. While on days when 129/130 don't operate - no need to rape Uzhhorod-Kyiv passengers in this day, so 13/14 on this day still operate on it's normal route.
It also explains why the detour to Chop has left - 129/130 don't stop in Chop (so it's not possible to coerce passengers from Chop to use 129/130, so passengers from Chop are not deprived). Also there is higher % of railroaders among Chop inhabitants, due to this many other in optimal and illogical things are done, for example 829/830 makes stop in Chop, despite only few passengers board/exit here.
So I dare to assert, that providing the direct train from Kyiv to Khust - Solotvyno was not the motivation, but only the pretense. Yes, local authorities from this area asked direct train to Kyiv, but they would ask it 300 years and don't get it in other circumstances. But now UZ needed the plausible excuse to deprive Uzhhorod for 1 train and used old request about direct train Kyiv to Khust and Solotvyno as a pretext.
If I understood it right, Peter's question didn't concern added through cars but the routing of domestic trains in their entirety.
exactly, and Ulf crearly realizes this too. But it's proper topic to ask other question, about validity of NRT ticket in NE trains, which Ulf asks.
so the answer is
Usual NRT ticket is valid in 129/130 and no additional supplement is needed.
Not only in case of hypothetical RIC attached to this train, but also if you travel in domestic cars too.
Anyway NRT tariff is higher than domestic tariff for NE.
Even in case of maximal possible discount by multilateral agreement - anyway NRT tariff + reservation costs more than domestic tariff+reservation.
For example 901-1000 km (distance from Kyiv to Uzhhorod via Vinnytsia - Ternopil - Kmelnytsky is 913 km) by UZ by NRT tariff cost 48 EUR. But you can buy ticket in country which gives some discount to UZ part according to multilateral agreement. AFAIK biggest possible discount are given by MAV (40%) and CFR (probably 50%, but it's uncertain, it's suggestion of Radan (based on price Suceava - Chernivtsi from .doc file from CFR website), which we hans't managed to check). So MAV definitely can sell NRT ticket Uzhhorod - Kyiv via Ternopil Pidvolochysk Koziatyn-1 and price should be 48*0,6=28,8 EUR. If the suggestion of Radan is correct - CFR hypothetically could sell same ticket in 24 EUR.
And it's possible to combine such ticket with 13-eur reservation and utilize for travel in 129/130, but anyway it will be more expensive than domestic ticket+reservation for 129/130 (~555 UAH=~19 EUR).