This passage of Scripture is relevant to Roman Catholic transubstantiation because it affirms that Jesus Christ is our source of spiritual nourishment. He is our spiritual food. He, the substance, is the same substance that is made mentally present by faith at the meal of the New Covenant.
Transubstantiation does not involve the eating and drinking of Christ in a "spiritual" manner. That language is distinct from Roman Catholic dogma. Transubstantiation takes place when the priest pronounces the bread and wine to be Jesus Christ's actual body and blood (the change is not in the accidents, but substance).
What matters in Roman Catholic theology is the participation in that physical substance. But this is directly contrary to the way that the Scriptures speak concerning the participation of those ancient people in the meal and water (in that case).
The Israelites "ate" and "drank" Christ, which must be spiritual and not physical because no transubstantiation took place during the Old Testament. We partake of Christ in the same spiritual way that the Old Testament Jews did.