It looks to me like the rootstock has suckered, likely because the graft didn't take. BUT, the good news is that seedling walnuts are usually decent quality, they just take longer to produce and size and flavor are more variable.
Nut trees, persimmons, and mulberries are all a little trickier to graft usually, as they like the temperature to be in the 70's during the day for about ten days after the time that you graft them. This is what one horticulturist told me. Another said they just prefer the rootstock to have broken dormancy.
When you reach your lowest point, you are open to the greatest change.
Now that I've seen the whole thing, I do think that is a failed graft and the rootstock has asserted itself big time.
It's obviously a vigorous tree. You can either let it go on its own, and plan to wait 10-15 years before you get much in the way of a harvest, or try to graft a new scion on it. Walnuts are tricky and all my reading supports what James said. The scion needs to be held in dormancy until the rootstock is just breaking. Warmth (around 25 C) during the callus formation stage helps immensely. On top of all this, the rootstock will pump an overload of sap into the graft union and if you tape it too tightly the pressure may force things apart.
I haven't successfully grafted a walnut yet, but I will be trying.