Objective, yes, he did commit a sin against the Holy Spirit. By being re-baptized, he implied by his actions that what the Holy Spirit did in his first baptism was not sufficient. Objectively, that is a sin, because it insults the work of the Holy Spirit. But it is not the same thing as the sin against the Holy Spirit—the sin of "blasphemy against the Spirit"—which involves a final refusal to repent.
By trying to be baptized again, your friend was expressing a willingness to repent and be saved, so clearly no final impenitence was involved. Even though your friend’s action was objectively a sin, he may have committed it in innocent ignorance, in which case God won’t hold it against him. The sin of getting re-baptized unconditionally would be a grave one, which means that it would be a mortal sin if the usual conditions were met. But he may have been re-baptized with sufficient ignorance that the sin would not have been mortal. Either way, what he should do is go make a good confession (Jn 20:21-23), and, whether the sin was mortal or venial, he will be forgiven.