To explain the numbering system: I've never seen this form of notation before but it makes sense, as long as you can figure out what key you want to sing it in.

Chords can be treated as notes of a scale, some are going to be major, some minor, and some are sevenths.

So the chart showing that C is 1, D is 2 etc. is just an EXAMPLE. The #1 chord/note aka the TONIC, is the name of the key you are playing in--obviously key of C in this example. But you can just as easily use G as 1, A as 2, etc, if you find that G is a better key for you to sing the song in.

The notation "57" means "fifth chord, played as a seventh"--so if you are playing in G, it's a D7. If you are in C, it's a G7.

The asterisks are like bar lines--they show how many bars to hold each chord for. Just keep on playing the designated chord until it changes. Looks like Wasn't that a Party is in 2/4 time, so you count two more beats for each asterisk.   

I know, when you say "aren't there any real versions", you would just like to see letter-named chords written out. But after you've sat through a few practices (specially band practices) where people keep saying, "I think you should try that in a different key", you will have scribbled so many chord names on the paper that you can't make any sense of it at all. So this system is worthwhile learning because it teaches an important priniciple of music. Many beginning musicians get fixated that whatever key a song is written in is the "right" key, and those are the only "right" chords. T'ain't so. The "right" key is the one that works best for the vocalist, and is achievable by the instrumentalists that are present. So a system like this, that shows the chords in a generic form, makes sense, you just need to get the hang of what the important chords are in any key.

In most folk music they are 1, 4, and 5, plus sometimes 2 (either minor or seventh) and 6 (minor).

Best
W-O