Depends which definition
of sport you use. You'll note that Amorous dalliance; lovemaking.
is an obsolete
definition. Being such an old-timer you might not have noticed, but currently used variations concentrate on competition in some way.
And while sex has been a competitive activity in some times and places (why does ancient Roman history come to mind?), most of us are more familiar with organized competitions in things like poker and bridge than in sex.
On another note, I must admit that I have to wonder why cards would be split out from games in general. Perhaps a sign of someone who takes "Go Fish!" waaaay too seriously?