I agree that he wasn't the "best player" on the pitch, in the sense of being the most outstanding or impressive performer, against either Bosnia, nor Iran. But FIFA's MotM award mainly seems to value "decisiveness" in a match (and considering that Messi scored the most important goals in those games, which were both solo efforts as well, it makes sense). Also note that Higuaín got the MotM award against Belgium (while I thought some of Argentina's defensive players were a lot more deserving) and Romero against the Netherlands (should've gone to either Mascherano or Vlaar, although the latter loses "points" for his missed pen. IMO), so it's not just a popularity thing. They clearly look at the player they think had the most decisive impact on the result, not necessarilly the player that performed best throughout.
My take on stand-out performers in each game,
Arg v BIH, 1. Besic, 2. Pjanic, 3. Messi
Arg v Iran, 1. Dejagah, 2. Romero, 3. Rojo
Arg v Nigeria, 1. Messi, 2. Musa, 3. Rojo
Arg v Swiss, 1. Messi, 2. Shaqiri, 3. Di María
Arg v Belgium, 1. Biglia, 2. Garay, 3. Mascherano
Arg v Holland, 1. Mascherano, 2. Vlaar, 3. Garay