That article seems to imply that it’s the priests and the laity who are under the jurisdiction of Latins.
That is true and a good distinction. Parishes, priests, and laity of the Russian Greek-Catholic Church are canonically subject to the Latin Ordinary w/in whose territorial jurisdiction they are situate. The Church itself is
sine episcopi - without bishops.
To answer your first query - that the Church has no hierarchs at present is a function of ecclesiastical politics. In 1896, Father Nicholas (Tolstoy), of blessed memory, a Russian Orthodox priest, presented in Rome and sought to enter communion. His request was granted and he was incardinated into the Melkite Patriachate (Why? No one knows with surety. Speculation includes the possibilities that the only EC hierarch in Rome at the time may have been a Melkite bishop or that Rome, not foreseeing that there would later be others, thought best to enroll him in the only Byzantine Patriarchate.)
The Church is usually dated to the appointment of Blessed Father Archimandrite Leonid (Feodorov) as Apostolic Exarch of Moscow for Russian Greek-Catholics. At the time, he was under the canonical supervision of Metropolitan Andrei (Sheptitsky), principal hierarch of the Ukrainian Greek-Catholics.
Subsequent to the martyrdom of Blessed Leonid, Blessed Archimandrite Kliment (Sheptitsky) was appointed Exarch. After he was martyred in 1951, the exarchate remained vacant - unless a successor was named
in peccatore and never revealed due to the Communist situation in the USSR.
A second exarchate was established at Harbin, China, to which many Russians had fled to escape persecution, The Servant of God Father Archimandrite Fabian (Abrantowicz), MIC, was the initial appointee to that See and, after his martyrdom, was succeeded by the Servant of God Father Archimandrite Andrzej (Cikoto), MIC, who suffered a similar fate.
Both exarchates remain listed in Vatican documents, but are
sede vacante and have been for more than a half-century. That either will be reconsituted any time soon is unlikely, as doing so would present a major stumbling block to relations between Rome and the Patriarchate of Moscow, which considers the Russian Greek-Catholic Church as an infringement on its territorial prerogatives and as poachers.
The last two hierarchs were Kyr Alexander Evreinov and Kyr Andrei Katkoff, MIC, both of blessed memory. Both were
episcopi ordinans, ordaining bishops, and neither held a title of canonical jurisdiction.
A Latin bishop was named Ordinary for Russian Greek-Catholics in Russia a few years - a situation known as being
sui alienis - subject to the law of another. It is an unsatisfactory situation created by Rome to avoid a move by Russian Greek-Catholic clergy to elect an administrator to the vacant exarchate.
why are they under the jurisdiction of another Church? I thought each Church is meant to be distinct from the other.
Good question … because Canon Law places Eastern and Oriental Catholics of a Church that is without hierarchy (or of a Church with hierarchy but resident in a country where their Church lacks same) under the canonical jurisdiction of the local Latin ordinary.
Or for that matter, why not have them under the jurisdiction of another Byzantine branch Church? It would relate with the Russian Catholic Church’s customs better than a Latin would.
A better question yet! Probably because, when the Codes were written, it never occurred to their Latin drafters. As a practical matter, this has occurred in several places - but as a makeshift arrangement in most instances. For example, there are 4 Russuan Greek-Catholic temples in the US. One is formally under the spiritual omophor of the Melkite Eparchy (albeit, canonically subject to a Latin ordinary); another is informally under the same omophor; a third is served by a priest of the Melkite Eparchy; and the fourth is under the omophor of the Romanian Eparchy, informally.
In Brazil, the sole Russian temple is informally under the omophor of the Melkite Eparchy and the same is true in Australia.
Hungarian, Croat, and Slovak Greek-Catholics in the US, who lack hierarchs, are committed to the pastoral care of the Ruthenians; the Ruthenians, in Canada, are commtted to the pastoral care of the Slovaks, while the Hungarians are committed to the pastoral care of the Ukrainians. Those arrangements are all formalized by decrees from Rome.
The Ruthenians erected a parish in the US for the Byzantine Italo-Greeks, who have no hierarchy in this country - that arrangement has become formal by default, given the erection of the parish.
The Melkites in Australia serve the pastoral needs of the Byzantine Italo-Greico-Albanians there, whose only hierarchy is in their historical lands. That is an informal arrangement.
The Belarusians and Albanians, likewise, have no hierarchs at present. The Albanians are, at least, under the canonical authority of a Byzantine hierarch, albeit he is not himself an Albanian Greek-Catholic. The Belarusians, in Belarus and the UK, are under the canonical supervision of Byzantine prelates of their Church, but they are not hierarchs and are, themselves, subject to Latin ordinaries.
The Georgian Greek-Catholic Church is extinct, having been without a hierarch since the martyrdom of the Servant of God, Father Exarch Shio (Bashmanshvilli) and having been without clergy of their Church for a half-century now.
One of three Italo-Greico-Albanian canonical jurisdictions is presently
sui alienis, subject to the hierarch of another Church, since the retirement of its hierarch a year ago.
Other than that, all’s well!