They might be just removing "to be", that's what I love about English you can break and abuse it and it still mostly makes sense. You could even drop the "the" and "-ed" from those phrases and most people would still understand what you mean by "dog needs walk".

yeah, they are just dropping "to be". But "dog needs walk" sounds wrong, whereas "the dog needs walked" sounds normal to the people who use it. I don't know whether there is a reason almost nobody says "dog needs walk", but I don't know much about linguistics :)

Northeast Ohio uses this construction rather than the “-ing” gerund. It took me awhile to change that when I moved to the East Coast.

Southern Hillbilly uses the same construction with a prefixed a: "This here dog needs awalkin'"