A lot of the answers focus on the word "date," and point out (correctly) that established couples also go on dates. I think this is a bit of a new usage, and intentional. But I want to point out the word "has."
When I'm going out with my wife, I'd say "I'm going on a date with [name]," or "[name] and I have a date tonight," or other such statements.
But when you say "[x] has a date with [y]," I would guess that their relationship is new, or even that this is a first date. This might not be 100% accurate, but it would be my first thought. This is because the use of the word "has" suggests some kind of attainment -- maybe [x] finally worked up the courage to ask [y] out, or they're back together, or whatever. But this is somehow surprising.
If I said "I have a date with [wife] tonight," that would imply (to a listener who is like me, I guess), some kind of freshness or excitement -- maybe we reconciled some major argument, or she just got back from a long trip, or whatever. I wouldn't say it for "we got a babysitter and we're gonna go see a movie." In that scenario I would more likely say "we're going out tonight" or even "we're going on a date tonight," but the idea that we would want to, or be able to, go on a date, is assumed.