I suppose you could move the concept to ASB, and ISOT the Americas of 66 million years ago to 1000 AD.
Personally I suspect the high O2 levels in the atmosphere had something to do with how the dinos could get so big. Still, elephants manage, and so do whales, so O2 access can't be the be-all and end-all.
Well, it's not the atmosphere, it was rather their lungs. Most dinosaurs, except for the ornithischians, did have bird-like lungs which are much more efficient than the mammalian ones. The ornithischians in turn did have more mammal-like lungs, and they were also on average smaller than the saurischians. Also, most ornithischians were quadrupeds, especially all larger ornithischians (think Ankylosaurus, Shantungosaurus, Stegosaurus, Triceratops) were all quadrupeds. In contrast to that, the theropods did have bipeds that were much larger (think Spinosaurus or Tyrannosaurus or Therizinosaurus), and in the sauropod lineage there were the largest land animals alltogether. Hence there is a strong case for this.
Now, in regard for the atmosphere, the oxygen level when the dinosaurs started out was actually lower than today. In the Triassic, there was very little plant life, neithor on the land because it was so hot and arid, nor in the sea because there were relatively few shelf areas (bear in mind that marine stratigraphy worldwide for the Triassic is lousy except for Alpine Europe). The latest I heard, oxygen level at the end of the Triassic was around 10%. Oxygen levels only later began to rise again when Pangaea broke apart and the climate became more humid.
So no, I don't think dinosaurs would have had any problems being gigantic in the modern world.