Sometimes languages develop diversity for other reasons than geographical separation. American English and British English have differences which were introduced by choice during and after the American Revolution (Revolutionaries made a point of eliminating the use of the letter "u" in words like colour/color, labour/labor and so on). French was a very disjointed language which was "standardized" during the French Revolution to make the "Parisian" dialect the "official" version of French, but even now French speakers in places like Brittany, Normandy or the Province of Quebec have very distinct pronunciations and dialects different from Parisian. For that matter, the UK is a very small nation, but the regional dialects between Northern, Southern and "London" English are pretty extreme (and that is before you start taking Welsh, Scottish and Irish speakers into account...). Working with British soldiers, I found them to be almost impossible to understand, except for the officers who spoke what we might call "BBC" English.
As peoples become more numerous, various regional dialects, slang terms and different rates of development and adoption of new technologies will cause the language to morph. They may all speak evolved PIE in your world, but regional differences may still make understanding PIE between PIE speakers as difficult as understanding Americans vs British vs Caribbean vs Indian English speakers today.
On a very technical level, your PIE speakers will have a common language and commonalities with some of modern Earth languages descended from PIE, but on a practical level, not so much.