My guess is this question probably concerns one of the main reasons of the split between the western and eastern churches: the filioque phrase. In the east christians believe that the holy spirit only derives from the Father, while western christians insist that it proceeds from both the Father and the Son. Rabban Sauma, being an 'eastern' christian, most likely wasn't completely up to date with how the holy spirit and its origin were seen in the west, and was probably interested in this difference of theological insight.

I'll flesh this out: Rabban bar Sauma, unlike the Cardinals he was speaking with, was a member of the Church of the East, often inappropriately called the Nestorian church, which holds a somewhat different account of the nature of Christ than the Latin Church. The Church of the East follows a theological account derived from the Antiochene school, especially that of Theodore of Mopuestia and his disciple Nestorius and systematized by Babai the Great, in which Christ's divine and human natures were distinct but united, as opposed to the Chalcedonian formula that Christ's human and divine natures were one and fused. To some extent this is a semantic and philosophical distinction, and modern proponents of inter-church dialogue have suggested that these are as much differences in linguistic formulation, but certainly these positions were seen as associated with more visible and visibly unpopular ideas like adoptionism. In addition, Bar Sauma was split from the Latins on the Filoque clause; although it was less relevant to the differences between the Church of the East and the Catholic/Latin Church* it still seems from this text to have been of some importance. Rabban Sauma is clearly here disputing with the Latins about the formulation of the procession of the father, the son, and the holy spirt, and the Latins are depicted as holding him in respect for his congent defense of his position(if you read carefully, you'll notice that he argues that the entire idea of one part of the trinity proceeding from the other is nonsensical) even though they disagree with his argument. I'm also intrigued by the fact that the cardinals don't pursue the questions of the nature of Christ but instead the filioque question; it may be that as the cardinals in question had more interaction with the Eastern Orthodox Church(not the same as the Church of the East, bear in mind) they were on some level more primed to ask about points of dispute with the Church of the East. It's also possible that Rabban Bar Sauma included this either because it was less germane of a question for the Church of the East(and therefore more remarkable to him) or because he wanted a good example of how to argue properly with someone of a different theological argument-that is, an example of the theological debate-disputation as a literary genre. In fact, the use of similes in this text makes me wonder if he isn't intentionally invoking the disputation as a model.

*Edit to be perfectly clear: The Church of the East is not, in fact, the same as the Eastern Orthodox Church and the filoque controversy was between the Greek rite churches lead by the Patriarch of Constantinople and the Latin rite church lead by the Pope; the Church of the East was not a direct party to the controversy as far as I know.