Did you order it under mail order delivery rules or under alcohol retailer rules? They're quite different. If the person you bought it from offered beer and alcohol as well, you were probably ordering under the retailer paradigm which requires an ID check. If you ordered it straight from a wine producer or exclusive wine seller then it was probably under the mail order framework. The point isn't that all wine purchases aren't ID'd, it's that there is a framework under which you can legally order wine online without an ID check happening -- if you pursue the alcohol retailer delivery rather than wine mail order route you might not be able to do that though.
Not in all states. In my home state of Pennsylvania, it's only legal to have alcohol delivered by the Pennsylvania Liquor Control Board. It is not legal to order directly from producers.
The laws do indeed vary by state.