I am not say that the Canons bind the Orthodox, but they do bind the Latin or Eastern Catholic who is seeking the Sacrament. I would be interested in what a bishop and/or canon lawyer would say to this question.
Perhaps canon 671 of the Code of Canons of the Eastern Catholic Churches, which I do not think has been cited, may be of assistance. It is the parallel of canon 844 of the Latin Church. Paragraph 2 is relevant to Catholics, although I do not know whether a Orthodox priest would be willing to administer the sacrament even if its condition is met from our point of view.
*§1. Catholic ministers licitly administer the sacraments only to Catholic Christian faithful, who, likewise, licitly receive the sacraments only from Catholic ministers. *
*§2. If necessity requires it or genuine spiritual advantage suggests it and provided that the danger of error or indifferentism is avoided, it is permitted for Catholic Christian faithful, for whom it is physically or morally impossible to approach a Catholic minister, to receive the sacraments of penance, the Eucharist and anointing of the sick from non-Catholic ministers, in whose Churches these sacraments are valid. *
*§3. Likewise Catholic ministers licitly administer the sacraments of penance, the Eucharist and anointing of the sick to Christian faithful of Eastern Churches, who do not have full communion with the Catholic Church, if they ask for them on their own and are properly disposed.This holds also for the Christian faithful of other Churches, who according to the judgment of the Apostolic See, are in the same condition as the Eastern Churches as far as the sacraments are concerned. *
*§4. If there is a danger of death or another matter of serious necessity in the judgment of the eparchial bishop, the synod of bishops of the patriarchal Church or the council of hierarchs, Catholic ministers licitly administer the same sacraments also to other Christians not having full communion with the Catholic Church, who cannot approach the ministers of their own ecclesial communities and who request them on their own, provided they manifest a faith consonant with that of the Catholic Church concerning these sacraments and are rightly disposed. *
§5. For the cases in §§2, 3 and 4, norms of particular law are to be enacted only after consultation with at least the local competent authority of the non-Catholic Church or ecclesial community concerned.
In the Latin Church, canon 976 has “Even though he lacks the faculty to hear confessions, any priest validly and licitly absolves from any kind of censures and sins any penitent who is in danger of death, even if an approved priest is present.” Eastern canon 725 is substantially the same (though I think the Latin is more elegant in the Eastre canon, but that’s just personal taste).
Divine law binds everyone. Merely ecclesiastical laws bind those who have been baptized in the Catholic Church or received into it, possess the sufficient use of reason and, unless the law expressly provides otherwise, have completed seven years of age. That in canon 11 of the Latin Code and in 1490 of the Eastern canons.
If a non Catholic approaches the Cathollic Church for the administration of a sacrament (or in the case of even a non sacramental marriage), our Church law would bind them in that sense as it would be applied to the situation.
Note that paragraph 2 speaks of particular law. So we’d also have to know about any legislation in a given Catholic Church of the East that might apply.