That’s a difference between theatrical audio mixes (Star Wars showed theatrically with three distinct audio mixes, depending on the theatre’s capabilities). The targeting computer sounds were in the mono mix, but not in the stereo or surround mixes. So if you’re listening to the 1977 surround track (a typical default because it sounds great on a modern home theatre setup), you’re not going to hear them.
When the Star Wars audio mix was revised for home video starting in 85, they brought some of the mono mix effects into the stereo/surround tracks. I’m not sure when they incorporated the targeting computer noises, but it was in one of those later revisions.
The mono mix is worth a listen if you haven’t heard it before. Yes, it’s mono and the quality isn’t as good, but it’s very different from the other mixes at times, and it’s just as “original”. In fact, most theatres at the time were equipped for mono, so it’s likely what most audiences heard in 77.