The ICRC considers the presence or absence of (governmental) consent to a third State’s military intervention to be essential for delineating the applicable legal framework between the two States. According to this view, even if the intervening State solely directs its attack(s) against a non-State actor present in the territorial State, ‘that intervention constitutes an unconsented-to armed intrusion into the territorial State’s sphere of sovereignty, amounting to an international armed conflict within the meaning of common Article 2(1).’ (from paragraph 260)

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This is relevant to the question whether or not the presence or absence of (governmental) consent is essential for delineating the applicable legal framework to an armed conflict (whether or not the (Syrian) conflict should be classified as a NIAC or an IAC).