According to the YouTube notes;
Sung by the Ensemble Organum, from "Chant Mozarabe Cathédrale de Tolède (XVe siècle)".
The chant is an heavily-abridged version of Daniel 3:49-52, 57, 88. These verses are not present in 66-book Bibles i.e. ones lacking the Deuteronicals aka the Apocrypha; note that this 'missing' section (comprising a total of 66 verses), also known as "The Prayer of Azariah and the Song of the Three Young Men", comes between Daniel 3:23-24 in the Greek Septuagint, and eventually, in Catholic and Orthodox Bibles (see here for example:http://www.usccb.org/nab/bible/daniel/daniel3.htm). This same section are also used as a hymn within Eastern Orthodoxy, the Church of England, and the Lutheran Churches.
Due to some priests leaving this hymn out, the Fourth Council of Toledo in 633 AD (Canon 14) decreed that the singing of the Hymn be made mandatory on all churches in Spain and Gaul during solemn Masses, citing the antiquity of the custom and that "the catholic Church spread out all over the world performs [it]":
"Ymnum quoque Trium Puerorum, in quo universa caeli terraeque creatura Deum collaudat, et quem Ecclesia catholica per totum orbem diffusa celebrat, quidam sacerdotes in missa Dominicorum dierum et in sollempitatibus Martyrum canere neglegunt. Proinde sanctum concilium instituit, ut per omnes ecclesias Spaniae vel Galliae in omnium missarum sollempitate idem in publico decantetur, communionem amissuri qui antiquam ymni huius consuetudinem nostramque definitionem excesserint."
As a final note, the version sung here is actually one of two found within the old Missale Mixtum: the one contained at the model Mass of St. James the Great – shown at the beginning of the video. The other – more complete, with a different preface – version is found within the propers for the First Sunday of Lent, while noting in the rubrics that it is required for the 'Sunday before the Day of Ashes' (Dominica ante Diem Cinerum)! This is where some inconsistencies abound, as one seems to infer that it was the exclusive feature of Lent, whereas other would imply that it was recited throughout the year.
The Missa Gothica seù Mozarabica, edited in Mexico by Cardinal Francisco Antonio by Lorenzana (later Archbishop of Toledo) in 1770, which follows the text of the model Mass, contains the text; but it is interestingly absent in the Rubricas Generales de la Missa Gothica-Muzarabe y el Omnium Offerentium (1772). The Hymn is also in the modern Mozarabic liturgy, the text generally following the fuller one found in the First Sunday of Lent in the old Missal, albeit now only recited during martyrs' feastdays