I know a lot of old shotguns have rare chamber lengths... but I'm no expert, so I looked it up. 10 gauge is/was offered in 2 5/8", 2 7/8", 3, 3 1/3". Cartridges of the World; by Frank C Barnes, 5th edition, page 320
So, YES, there were 2 5/8" shells.
Guns made for roll crimp or just an over shot wad, would have different barrel chamber dimensions than those made for modern shot shells where the crimped end would need room to open... and be prevented from over expanding to allow extraction. It does seem odd that the bore is cut wider in this way beyond the chamber, but these were built to be blank guns.