Importance is I guess in the eye of the beholder, but it's pretty hard to argue that Christian Western Europe isn't a particularly large part of the Greco-Roman world.
The argument was that it wasn't particularly large or important.
It's pretty easy to make this argument: In terms of the known world during Greco-Roman times, most of the known world was to the South and East. Persia and Carthage were major empires, and writings from those parts and beyond were known in Rome. Compare that to Western Europe: The Romans barely knew that Britain existed before Julius, and it was so unimportant that they abandoned it. Gaul was geographically a large part of the empire, true, but wasn't particularly important. Note that land grants to legionaries were given in Romania, because Rome wanted to control that area rather than in Gaul.
Counter-factual histories are endless of course, but it can be worthwhile thinking about them occasionally. We live in a world where the Mongols stopped before Vienna (at least partly because they didn't see anything rich enough in Europe to bother with). If they hadn't stopped, or if they hadn't destroyed the Islamic world and inland trading empires like they did it is entirely possible that Western Europe would still be considered a backwater.
> Note that land grants to legionaries were given in Romania, because Rome wanted to control that area rather than in Gaul.
This isn't really true at all. By the time Trajan conquered Dacia (and distributed land to his veterans there) Gaul was a settled, integrated part of the empire.