None of this is relevant. Every player has a mental image of the ogre in their head. For some players the ogre might be holding the club in it's left hand, for other players they might have a mental image of an ogre with a club in it's right. Since it has no gameplay effect the DM didn't mention it, but if you could look inside every players head you would see they are all watching slightly different TV shows.A couple of observations that I find interesting relating to that. The first of course is that a model should contain less information than the thing it is simulating. The choice of what to include depends on goals: RPGs have converged around attack chances, hit points and such like. So as you point out handedness is excluded.
Intriguingly, unless someone at the table added left or right handedness to the fiction, that literally doesn't exist. It's not in the model, and it's not in the fiction. The ogre only exists to the extent to which it is articulated... because we don't need a real ogre to have a fiction about an ogre. Therefore the ogre handedness can't possibly exist unless we describe it. I don't claim we couldn't describe it, or even that it's not part of our ideas about ogres, but it does not exist in our fiction at the table until we call it out. Smell likewise, and so on.
None of that matters until the player tries to do something that involves interacting with the environment. For example "I try to jump over the ogre's head to get behind him". The rules cover how high a character can jump, and the player should know how tall their character is, but the DM suddenly needs to decide how tall the ogre is and how much clearance there is between the ogre's head and the ceiling. They need to do so in a way that is as consistent as possible with all the different mental images that the players have.