The game was called Obliterate, and it supposedly ran on the UK Prestel dialup service. The following clipping is from Time Magazine, according to https://cronotripper.substack.com/p/malvinas-y-los-videojuegos-cenizas
I also found the following story in the August 1982 edition of 80 Micro:
The game (though not the controversy) is also referenced in the following US news article, dated 10th April 1982: https://www.upi.com/Archives/1982/04/10/New-video-war-game-features-Falkland-Islands/7638387262800/
The game, which is available in Argentina, Great Britain and the United States, is offered by Prestel, the world's first home-computer service, operated by British Telecom.
The computerized data base of the game, along with the firm's other services, are hooked up to home TV sets over telephone lines.
'Obliterate,' introduced to the Prestel database three days ago, pits the British Royal Navy against the Argentine fleet in the Falklands.
Elements of the game are updated each day based on news reports of British and Argentine plans and military movements.
If a viewer, for example, blows up an Argentine ship, the screen flashes: 'Well done, sir! You have achieved your mission to obliterate the pride of the Argentine fleet. You are a national hero. Horatio would be proud of you.'
About 16,000 British viewers pay for the service, which includes the game.
The service also is available in Argentina, but it is not known how many people there had signed up for 'Obliterate.'