The author believes Alexander’s conquests constitute a reason to think he was great. This doesn’t imply the author believes one cannot become great through other methods besides conquest.

The author overlooks the possibility that there are larger tombs in the region that we just haven’t found. If that’s true, we can’t conclude the largest tomb found so far must be Alexander’s. So the author must assume the largest one found so far is the largest that existed.

How tombs in other regions compared to this tomb doesn’t affect the argument, because we have no reason to think tombs in other regions are relevant. The author’s assuming Alexander’s tomb was in the region we’re talking about.

The argument is concerned with whether a particular tomb was Alexander’s. What happened to Alexander’s empire after he died doesn’t affect the reasoning. We have a premise that says Alexander was the greatest Macedonian; what happened to his empire doesn’t change that fact.

We know the recently discovered tomb is the largest found in the region. Whether we determined the size from remains or from something else doesn’t matter. We know it’s the largest found, so questioning this fact isn’t where we’ll find a flaw.