I doubt that it has any doctrinal force other than the fact that it restates accepted Church doctrine. It’s most likely a private letter expressing his hopes, thoughts and opinions in regards to reuniting with the Eastern Orthodox churches. It would be wise to consider what he has written and consider it, but it was not intended to be something that rises to the level of an encyclical or something meant for the priests and bishops of a particular country or region.
Just consider the difficulty of even finding a translation of the letter or that it appears to only be online in the Acts of the Holy See and not available in any sort of translation.
ChadS
It was not a private letter, but to the entire Church, that Pope St. Pius X wrote in response to a journal article that was full of serious errors. In the letter he instructed that the letter be translate and communicated. It was published in the AAS the official publication of the Holy See.
Extracts:
“…, in a review of recently published,
Roma e l’Oriente, appeared an article which causes us great grief. It was titled: «
Pensées sur la question de l’union des Églises» “Thinking about the question of church union”]. This writing is full of so many and so serious theological errors, and even historic, it was difficult to earn more in fewer pages.”
…
“You take care, Venerable Brethren, to translate this letter carefully in the language of the area entrusted to you and spread it. In announcing with joy that the dear author of this essay, written with lightness but with good faith, signed sincerely and wholeheartedly to the doctrines set our presence in this letter and expressed his willingness to teach, reject and condemn the rest of his life all that the Holy Apostolic teaching rejects and condemns, as a token of divine favors and as a token of our benevolence, We grant you affectionately in the Lord’s Blessing.”
…
“Given at Rome at St. Peter XXVI day of the month of December in the year 1910, the eighth of my Pontificate.”
(It may be currently supressed to help in the Catholic-Orthodox dialog.)