Oh, I had a set of those too! Never really did much of anything with them, but I remember them and that box and everything.
On looking at your link, that’s the exact set I had, not a Domino Rally set.
The frame and cardboard mechanism was awful and never worked quite right, just trying to get it off when you were done setting up meant knocking at least a few “dominoes” over. Also had the “whole house except kitchen carpeted” problem and compounded it with “lumpy uneven linoleum” in the kitchen. I never did get anything set up quite right with the thing.