NTR or
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, (
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. 寝取られ, 寝(ne) as in 寝取られ means "sleep", in this case, "
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sleeping with someone (cheating)". 取られ(torare) is a noun coming from 取られる(torareru), "have something stolen/robbed". - Urban Dictionary
Sure seems like the princess isn't the MC's lover, so no NTR
¯\_(ツ)_/¯
And just because a ton of ntr doujins might use the tag doesn't mean that it's actually NTR, just like if someone writes the word blue on a red door doesn't mean that the door is suddenly blue.