Back in the CRT days, TV screen sizes were constrained by power supply requirements and the weight of the picture tube. Hence the marketing appeal of products like this:
I love the hyperbolic visuals of these old ads -- they couldn't lie, really, but they could certainly make it look more exciting than it was likely to be in reality. Note that the alien co-pilot appears to be the illegitimate offspring of Skeletor from Mattel's Masters of the Universe toy line and Ray Harryhausen's Ymir from 20 Million Miles to Earth. The spaceship also has a really amazing viewport system, capable of observing the player's ship from a third-person view, several miles away, especially considering that the ship's onboard computer appears to be an Atari 2600. The screen display uses (with Atari's permission) the official artist's rendering of Asteroids -- not an actual screenshot -- so there's no actual representation of the product in this ad at all!
The omission was good for sales, because the Beam Scope never worked very well -- the magnifier was just a large fresnel lens mounted in front of the TV screen. Viewing angle suffered badly, dimness was a problem, and it could only magnify to a certain degree before radial distortion became an issue. So you could enlarge a 20"-26" screen up to 30", but that was about it. And of course the scan lines, RF converter noise, and analog color TV blurriness would also be magnified -- early 80's videogame graphics weren't necessarily meant to be seen writ large.
The Beam Scope product line was actually sold by a couple of different advertisers back in the day, with big, full-color ads from International Marketing Services and smaller black-and-white spots from Diaco Sales. The ad artwork and copy were largely the same from both marketers.
I was surprised to discover that the Beam Scope product line is actually still on the market, currently sold as an aid for the visually impaired. Looking at the current product descriptions, the "doubles the size of your field of play!" claim in the old ads seems a bit fishy -- I suspect they meant you could double the size of the portion of the screen used by the actual game display, or else they have retired the more extreme and unwieldy Beam Scope sizes as real display technology has evolved.