The 26-year-old was using the Twitch video platform to broadcast himself playing the popular shoot-'em-up survival game Fortnite when the alleged assault happened on Sunday night.
Footage shared on Twitter showed the man, who was not named, shouting to someone offscreen "I said I'll be out soon" before moving away from the computer monitor.
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A woman's voice is later heard saying "woman basher" and yells "you hit me in the face, don't you dare touch my face, you hear that, all you people there?"
The argument continues, with further yelling and crying offscreen as the man moves to and from his monitor and shouts "leave me alone".
In a second video, more yelling is heard between the pair as a child nearby cries.
Both videos were retweeted thousands of times on Twitter.
New South Wales state police said someone watching the live feed called officers, who arrested the man at his home in the southwest Sydney suburb of Oran Park on Sunday.
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He was charged with common assault and bailed to appear in court on Thursday.
Police also served him with an order which prohibits him from harassing, threatening and intimidating behaviour.
Police added that two girls -- aged three and 20 months -- were in the home at the time.
The 21-year-old woman was "not seriously injured" but was "distressed and shaken by the incident", they added in a statement. Local media reported that she was either his partner or wife.
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