He's right - without Greece, there won't be Rome. But I'm sure we'll just be as advanced. Maybe some other power will take their place, who knows.
But how can there not be Greece?
Even if the Greeks lost that war, they will be too rebellious to contain. Remember that the Persians didn't really have a very unified empire, and instead they had satripes that collected money from each province or peoples. Even though the Central Asian regions had centuries of warfare and cultural assimilation (Elmites, Assyrians, babylonians, Sumerians, Persians...) and their cultures were similar, they didn't manage anything more than a loose control. Remember their empire is HUGE.
Their control over the "Greek" colonies that they had wasn't exactly stable before the Persian wars either. Note that the administrative power of the Persian empire at that time was clearly the most advanced in the world. Seriously, no-one else could possibly field 180000 fighting soldiers (not counting camp women, slaves, blacksmiths or other support personnel!!!) across Central Asia for thousands of miles to Greece, carrying all the food, water & fodder for cavalry, cleaning up all the waste products, or even just manage the chain of command for keeping track of such a large mob.
My point is, their empire was far too large already, Greece was too far from Persepolis, and that mighty empire can stretch it's power no more. If the Greeks lost the Persian wars, the cities will mass revolt so much that the Persians will lose those cities AND the "Greek" colonies that they had a hold of. Attacking Greece was a dumb move to begin with. Why didn't they go for India instead?