I don’t think it’s bad grammar though, but may be a legacy of when people shopped locally, before big commercial companies set up supermarkets. In those days you would nip down to e.g. “Paul’s”, or “Auntie Joan’s” to pick up your groceries etc. because you knew the owner, often a local legend, of the corner shop by name. Now Tesco, Asda etc. are the owners so it has just continued. That’s my theory anyway but even if it’s wrong, I still say it’s acceptable grammar, even moreso if it’s regional patois which deserves preservation.
“McDonald’s” is the same principle. It is the official company name but denotes that McDonald possesses something, in this case, “restaurants”, so when you go to McDonald’s you infer the place you are going to. Same with Tesco’s, Asda’s etc. but strangely not Lidl (for me anyway).