After Googling Atlatl, I see I got the name completely wrong. I do stand by my description of the game, and Googling led me to believe I was describing Jai alai or pelota. The basket like device I was thinking this is is called a Chistera/Xistera. But given a closer inspection of the game and pictured object, it seems improbable that something so heavy could ever be used to play this game. But I did learn something, so that's good.
it's an Atl-Atl (I think). Without Google, I can only say that I vaguely remember it as something like grade-school "wall-ball" or squash, where you're constantly throwing a ball against the wall, using the pictured device, and someone else catches it and throws it back. Scoring, etc. are completely lost on me.
In any case, am I the only one who don't think that doesn't look much like Chuck Norris? I guess that what happens with aging...