I agree with Zeno. The horizontal oscillator is so far off frequency it isn't funny, and yes, this can be caused by kids messing around with the oscillator coil. Turn the slug back into the coil until the picture comes back. As you adjust the slug, the number of horizontal strips will slowly decrease until the oscillator is on the correct frequency (15,750 Hz) and the picture is normal. It wouldn't hurt to replace the HO tube while you're at it, although if the set makes a good picture once the oscillator is set properly, a new tube isn't absolutely necessary.
BTW, your Zenith TV is one of the early 1950s "porthole" sets. (VK member John Marinello's avatar is one of these, "The Byron" from about 1951.) Get yours working well and it will serve you well, with a DTV converter box or cable box, for many years to come (don't try to connect an antenna directly to the TV's VHF antenna terminals--it won't damage the set, but you'll get absolutely nothing but snow on the raster and white noise in the sound, since all TV is digital these days, except for some cities which may still have one or two analog stations). Zenith was one of the best TVs made in the 1950s through about the '80s, second, IMHO, only to Magnavox and Andrea, the last being a now long defunct New York City-based TV manufacturer of the late '40s through the fifties.
Zenith's slogan was "the quality goes in before the name goes on", which was true of their TVs from the '50s until the Gold Star era, which began in the late '80s.
The last few years of the decade of the 1980s were, unfortunately, the beginning of the end for once-proud Zenith. The quality of Zenith electronics (radios and stereo gear as well as televisions) took a heck of a nosedive, and never recovered.
The Zenith brand and logo, which continued to appear on Zenith color TVs from the '90s through the early 21st century (which were fraught with problems, such as CRTs that shorted after two years, taking the entire video chain with them), had been reduced to a mere marketing symbol. The company is now completely out of business, never to be heard from again.