This is "X Multiply," a side-scrolling shoot-em-up released by Irem (perhaps best known from another stylistically similar shooter series, "R-Type") in 1989. The characteristic "tentacles" extending from the ship are quite distinctive. I saw the tentacles and knew that I had played this game; however, I have played a lot of old video games, and it took me a little while to track down the name of the game and addition details about it.
You can see a complete playthrough of the Playstation re-release on YouTube. The magazine image is from level 6.