Thanks everybody for the comments!
I guess like Terry from Iowa said "...the mystery deepens."
On the "sandblasted" comment....
I think it would be extremely difficult to sandblast the piece while it is cooling without it changing the shape, or having pieces of sand be inbeded inside.
I would tend to agree with Adam, that if the piece was sandblasted, it was the mold itself, not the piece.
Going in a different direction with this...
I had mentioned the texture as "machine made" at first, and I still think this could be the case.... Does anyone know if Glass itself was worked in the same way that enamels and metal were etched for decoration? I know i have seen in the Antiques Road Show (US and UK) pieces of enamel, silver, gold, and metal-work finely etched, both manually and by machine. Mostly done for background decoration on enamels and clock faces....
Could this have been done to the mold of my vase?
I dont know how well the Glass industry and the Metal-work industries worked with each other during the turn of the century (1800-1950), so Im putting it out there.