You know what a cassette is. I don’t need to call it a cassette tape do I?
When they were widely used, people called cassette tapes “tapes” (common) or “cassettes” (less common). I don’t recall anyone calling a VHS videotape or VCR “a VHS”.
Similarly, I have seen people recently say “a vinyl”, which wasn’t ever the way it was said. (it would be music “on vinyl” or “a record”).
The only time I have ever in my thirty years of life heard someone refer to a VHS as a “videotape” or “tape” is in the context of “tape that show for me”. It’s always been “Video” or if they’re specifying the format “grab the videotape” or “VHS” a lot like how people today say “DVD”.
I think we’d both agree someone who calls a “DVD” a “DVD Disc” insane and someone who just says “Disc” could mean CD-ROM, Blueray, so forth. It’s too general and I think the same thing applies to “tape”.
Yeah, “video” was common, but “VHS” wasn’t. Maybe kids who developed language as the format was expiring in the early-mid 90s didn’t have lots of examples and just thought the letters printed on the tape were a noun.