There is a New York Times article (The Game Turns Serious at Atari from December, 1982. One quote from it is:
Atari is also facing problems in its two other businesses. Its arcade game business has dropped into the red this quarter and its home computer business, which has never yet been profitable, faces a market-share battle.
(the first business is the video game cartridge business).
With respect to operating profits, one gets
According to estimates by Mr. Simon of Goldman Sachs, cartridge sales accounted for $180 million of Atari's $280 million in operating profits in 1981.
So, video cartridges were king, arcade was the rest, and home computers lost money. However, the arcade division was in decline:
A problem getting its own games to market also has hurt the coin operated game business. "The fourth quarter of 1981 was, by a considerable margin, the best quarter in the history of the coin-op division,'' Mr. Gerard told analysts. ''The first quarter of 1982 was very good. The second quarter was a good quarter. The third quarter was a rotten quarter and the fourth quarter is a disaster."
They had high hopes for computers:
Atari's future may lie with its home computer division. The market for home - as opposed to small-business computers - has taken off this year and Atari has seen its sales quadruple, to an estimated $300 million. Yet the division is still losing money, perhaps $25 million $50 million this year.
Either way, since the home computers were losing money in December 1982, Atari clearly had more profit from arcades than computers, but game cartridges were still the money cow (for just a bit lonter).