No one here can be certain of what Apple might or might not approve, but an app that solely wraps a website isn't going to be highly viewed by the app reviewers, per what's in the previously-cited app store review guidelines.
Side-loading apps isn't typical on iPhone or iPad, and is not something that most users of Apple platforms would do or would even experience. Android users can get in trouble with side-loading sketchy apps, too.
It is possible to have low-volume distribution of apps from the app store, but that doesn't fit here, and—again—it is unclear what Apple might approve here, and this app looks like a whole lot of work at risk of not getting approved, and of not adding anything past what the website itself can offer the vendor and the vendor's customers.
A QR code can bring the user directly to the website, and the website can then provide specials, sign-ups, online ordering, and the rest. With the permission of the users, notifications of specials or whatnot via push, or via email.
Were I the store owner, I'd want to spend more time with the website and what's possible there—which is generic, and its contents and displays and behaviors are also more directly under my control—than with apps for the various platforms.
Beyond a traditional adaptive website design... Maybe... Maybe... Websites and webapps? It's quite possible to download anything from a rudimentary to sophisticated webapp from a website, though that's a somewhat larger investment than traditional straight HTTPS and JavaScript website design. But what's possible here is in the same range as an app for Apple or Android. For example, the entire Linux operating system, BSD, and a number of other Intel x86-64 operating systems can be booted entirely within a web browser, and some: more info. (And to be absolutely clear, I don't expect the store owner would ever remotely want or need bootable Linux in a web browser, this example is provided solely for you and for others reading here to better understand the scale of what's possible within a modern web browser, without dealing with an app store. Oh, and most of us would prefer not to download Linux over a mobile data plan.)