No, you don't have a Beatles-signed album. My guess is that a friend wrote the signatures on the album of a besotted fan to show their true devotion, something many of us did back in the day. This was the mid-sixties and we lugged our LPs along to any basement party (much like the ubiquitous iPods a few years back). We had no idea these records were finite or would be the sought-after collectables 40-50 years later.
That's also why you'll find many of these old album covers scrawled with boyfriend or girlfriend names or initials, drawings, stickers or personalizing notations.
It was also a method to determine ownership because at the end of most parties, there were frequent arguments of who's 45s or LPs belonged to who! Personalizing the covers neatly resolved the problem.