Answer

He is certainly disqualified according to Rabbeinu Hananel, though perhaps not disqualified under the law of a robber. Jewish law is ruled in accordance with the "some say" opinion there, and that opinion holds that he is disqualified from testimony. True, in the halakhic authorities it appears that the case is one of degrading eating, not disqualification as a robber. But according to Rabbeinu Hananel, this is a disqualification of robbery for less than the value of a perutah. In Rabbeinu Hananel’s second answer, however, the case is theft of something about which the owner is not particular, but that does not necessarily mean he disagrees with the first answer.
The medieval authorities (Rishonim) disagree whether there is a prohibition of theft for less than the value of a perutah. See Maimonides, Laws of Theft 1:2 (though it seems that according to him it is only rabbinic), who wrote that one violates the prohibition thereby, as opposed to Rashi on Sanhedrin 57, s.v. "Pain at the moment."
However, on the face of it, a Jew waives a claim to less than the value of a perutah, so even if there is a prohibition of theft, it is waived, and therefore Maimonides wrote that it is only rabbinic.
In any case, it follows that there is no Torah-level prohibition of theft here, and therefore the disqualification from testimony is not on account of the usual status of a robber but rather an additional disqualification, exactly as implied by the wording of Tosafot.
By the way, the next answer in Tosafot may also go in the same direction, except that it only explains how theft of less than the value of a perutah happens (for example, someone tasting from the sellers in the market).