Monica,
On the 1905, I am not certain but I think the way it reads, John Stevenson, Miner, may be Propretor of numbers 5, 6, 7, 8.
And I have just been looking at the 1915 Rolls, probably at the same time of you, and there were quite a few Stevensons living there, and John Stevenson seems to be Proprietor of 10, 12, 14, and 16. I think I can see why it might be talked about as being "Stevenson's Place" instead of Muiredge Terrace.
I went through 91 pages of the 1915 Rolls, searching for "Stevenson's Place" and I didn't see it. So maybe Muiredge Terrace is correct.
I live only a mile from that building and when I was a boy, I used to be able to take a short-cut through a large underpass that cuts right under the houses like a tunnel. The short-cut brought you out onto Main Street, Baillieston right next to the house named "Edelweiss" where the Templetons used to live.. You can't take that short-cut any more!