First I thought it was for some other musical instrument (guitar?) but both the title and the shopkeeper told me that the music sheet was for piano.
The diagram shows how a guitar player of moderate skill could play the indicated chord. Many guitar players have some chords they could play given just the name (generally C, G, D, A, E, G7, Dm, D7, Am, A7, Em, E7, and B7) but would not know how the fingerings for other chords. A different voicing for the Db chord (X-4-3-1-2-1, with the index finger playing both first-fret notes) would sound better, but would be harder to play. Some chords like A7 can be played in more than one way, and some sheet music will use one or the other depending upon what will work better in a given context, but I suspect many chord diagrams simply plunk on a typical fingering for each chord without regard for what chords appear nearby.
They're "guitar chord boxes". Remarkably useless objects. They rarely indicate anything more than the first entry for that harmony in the "book of chord shapes" with no thought of voicing appropriate to what comes before or after. But I suppose for guitarists who just want to "strum along", don't know their chords and don't have a book...
You'll find older music with 4-string shapes. These were for ukulele.