The first ever officially licensed movie based game. Based on the movie of the same name, developed and published by Atari. Released in 1982. Designed by Howard Scott Warshaw, who for inspiration would walk around Atari’s offices wearing a Fedora hat and cracking a bullwhip.
Source: Raiders Of The Lost Ark – Atari 2600 | Little Bits of Gaming
I believe E.T. actually beat out Indiana Jones in terms of release date by a couple of months and had many of the same kinds of elements. However, E.T. also has a reputation as one of the worst games ever released on the Atari 2600. To some extent, Raiders of the Lost Ark succeeded where E.T. failed but only to a limited degree. Raiders of the Lost Ark was not known as a great game either.