Hi Inma fdmaxey already answered this extremely well, but it took me ages to write an answer, so I'm giving it anyway: Yes, outdrew is grammatically as you have already guessed. In English, you can sometimes use the prefix 'out' to mean to do better than, or exceed. Commonly , you will see it in the verbs like outdo, outmanoeuvre, outflank, outsell, etc etc The sentence that you have quoted is probably using the word metaphorically, not literally. A draw is something that, for instance, an American cowboy would do - it is the action of pulling a gun from a holster and aiming it at the target. When fighting a duel, two men would face each other and attempt to be the fastest to draw their gun - because the fastest 'on the draw' would be more likely to shoot first and win the competition. The loser is 'beaten to the draw' or 'outdrawn'. An example: "The sheriff outdrew the bank robber and shot him dead."

"Draw" in this refers to drawing (taking out) a pistol from its holster. In American Western films, you will often see two men (one "good", one "bad") facing each other with pistol in their holsters. At some signal, they will pull (draw) the pistols from their holsters and try to shoot each other. To "outdraw" someone means to get your weapon out and fire it before your opponent does. "Outdrew" would be the past tense of "outdraw". "Draw" can also refer to any weapon in a case or holder - "Draw your swords!" means take your swords out of their scabbards (holders) and get ready to fight.