RE is a regiment.
Dispatch riders were part of signals, which at that time wasn't independent but part of Royal Engineers, so that's what I think "RE" refers to in this case
If you have his record it will say if he went overseas. Also if you have found a medal card it will confirm he served overseas. Post his name and number if you need help.
Unfortunately the only military record I have for him so far is, as I said, this badly mangled "attestation" record, a kind of signing on. Even his number isn't clear: 3??701 is the best we can do. Thomas Watson, born 7 Feb 1896.
BTW...he would have been conscripted.
Not in Ireland. There was legislation, passed in the teeth of great opposition late in the war, but it was never put into effect.