How would that be looked at under US "contract law"?
Contract law normally isn't implicated by shoplifting. There is no agreement of the parties in those cases.
The private lawsuit causes of action belonging to a category of civil lawsuits called "torts" arising from shoplifting would typically be called "conversion" (for money damages at common law), "replevin" or "claim and delivery" (to seek return of the specific items stolen), and "civil theft" (where available, normally providing both remedies and additional statutory remedies like attorney fees not otherwise available, not present in all states) (replevin is really, strictly speaking, a "property rights lawsuit and not a tort lawsuit).
As a practical matter, however, the criminal justice system is the easier, cheaper, and predominant remedy as a theft conviction ordinarily includes a restitution award to the victim, and the case is investigated and prosecuted at state expense rather than the merchant's expense. Usually, shopkeepers form a close relationship with local law enforcement agencies to make shoplifting and dine and dash prosecutions go smoothly.
If no such cases exist, then is there no contractual obligation
violated as a result of shoplifting or restaurant dashing?
Shoplifting doesn't violate a contractual obligation unless it happens after checkout but before payment.
Restaurant dashing would ordinarily be a breach of contract in addition to conversion, civil theft, and a crime, since by ordering food you agree to pay for it.
Note also, however, that if you order food at a restaurant and intended to pay and in good faith believed you could pay, but then realize that you don't have enough money (e.g. your only credit card was denied and you had no cash because the bank reduced your credit line without telling you) and admit that you can't pay, that rather than dashing, you do have a breach of contract claim for the merchant.
Historically, this situation is most often resolved with either an IOU from the diner (perhaps with a driver's license or something else of value offered as collateral for the IOU debt), or with payment in kind through washing dishes, and almost never results in actual litigation.
If such cases exist, then what are some cases?
I've never seen such a case at the appellate court level where cases are reported.
The criminal justice remedy is predominant.
Also, small civil claims are usually appealed to general jurisdiction trial courts whose decisions aren't reported publicly.
Almost nobody is willing to spend the money to use the civil litigation process in cases that are typically under $100 when there is no cost effective way in the "American rule" system where the loser doesn't usually pay the winner's attorney fees in a breach of contract case involving an oral contract, to litigate such cases.
Is there an implicit contract underlying any retail store transaction?
Yes. A contract for the sale of goods is governed by Article 2 of the Uniform Commercial Code in the United States. But, in a shoplifting case, there is no retail store transaction.