"Play of gazes" is not, I grant you, an expression much used in everyday speech, but it is much favoured by art critics to refer to people in paintings looking at each other. And I think that's what "trajets" refers to, as mchd suggests. Of course the expression in their eyes is eloquent, but "trajets" is more than the expression, it denotes the direction of the gaze. This is about how Joachim and Anna are looking at each other, what their looks express, not vis-à-vis the viewer (though a play of gazes in a painting certainly can include the viewer), but each other. So I see it. And let's recall that this is part of an argument refuting Vasari's reservations (or whatever) about "la place occupée par le regard dans la répresentation giottesque des sentiments", so I think this interpretation is thoroughly relevant in that context.

"Gaze" is a word art critics and curators love.

Here are a couple of illustrative examples:

"The triangular play of gazes, in which Isherwood stares at Bachardy and Bachardy scrutinizes Hockney, encapsulates the intense and stimulating friendship the three enjoyed"
David Hockey and others, David Hockney: Portraits, p. 1973
https://books.google.es/books?id=d9C5Xnv0KowC&pg=PA1973-IA12...

"The gaze
At the heart of the painting is a complex play of gazes enacted by the two figures seated in the theatre box."
On Renoir's La Loge
https://courtauld.ac.uk/learn/schools-colleges-universities/...

"Consider in this regard the picture's play of gazes. Not only does the executioner contemplate his victim, but the victim contemplates his executioner."
Marc Gotlieb, The Deaths of Henri Regnault
https://books.google.es/books?id=5Tg8DgAAQBAJ&pg=PT136&lpg=P...


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Note added at 10 hrs (2018-07-07 20:23:00 GMT)
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I said that it refers to people looking at each other, but not only. To me it's clear that Anne is looking at Joachim here, and quite intensely, but you might argue that he is looking not at her but beyond her. However, that situation can still be described as a "play of gazes". In the Renoir example I cited above from the Courtauld, "an elegantly dressed woman lowers her opera glasses, revealing herself to her admirers in the theatre, whilst her male companion trains his gaze elsewhere in the audience".