Steinbeck gets the phrase "in dubious battle" from a line in John Milton's Paradise Lost (I.104). In that passage, Satan is talking about how he fought with God, lost, and wound up as King of Hell (not as great as it sounds).
While it's difficult to know the precise reasons Steinbeck chose this phrase for his title (check out the our "What's Up with the Epigraph?" section to find out more), there's definitely something questionable about the fight being waged in this novel. The big question is this: who really wants this war in the first place?
Mac likes to remind London and the other men in the camp that this is not his strike. He insists that it belongs to the discontented workers, and he makes a big show of having London take votes every time he means to take action. But we know that Mac and London are manipulating the emotions of the disgruntled men to foment rebellion.
So do they really want the fight? It's hard to know. And that is precisely why this battle is a dubious one—kind of like that more epic one in Heaven.