Per a Vegas police report, obtained by TMZ, Wynalda -- who was coaching his son's club team in a recent tournament -- allegedly exchanged words with a player on the other team ... who claimed to cops that Wynalda called him a "bitch," insulted his mom and more.

The player told police he and the coach got face-to-face and he (meaning the kid) ended up shoving the coach ... which led to a fight breaking out between the two sides. The teenager alleges he got scratched amid all this ... but said he wasn't sure if it was EW or the players.

In any case ... a parent from the team ended up calling 911 afterward to report the whole thing.

TMZ has obtained video from the alleged incident ... which sources tell us shows how the whole thing kicked off after they say an opposing player took out Eric's son with a hard foul.

We're told the young Wynalda was sidelined for the rest of the match ... and, opposing players allegedly started to talk trash to EW -- who ignored them and simply wanted to get on with the game.

The video then shows a player approaching Wynalda and shoving him while another appears to throw a ball that hits him in the face. Our Eric sources say he kept his cool during the incident and didn't assault anyone despite the battery report ... and FWIW, the video seems to confirm that.

Eric's a bit of a legend in the U.S. soccer world ... bouncing around in the United States and abroad for almost two decades, and scoring 34 goals in 106 appearances with the United States Men's National Team between 1990 and 2000.