I must say I think that chart would confuse, rather than enlighten, a beginner - includes the proverbial 'more than you wished to know', to my mind.

The point is, that whatever key you are in [assuming for the moment that it doesn't modulate major/minor which only a minority of tunes do]: the chords of the tonic [1st degree of the scale], subdominant [4th] and dominant [5th] will contain all the notes of the scale between them; so that these three are all you will need to provide a satisfactory accompaniment. It is also useful to know that if you play the dominant [5th] with that added flattened 7th (G7 in the key of C, for instance, instead of G-natl), it has that nice effect of implying a return to the tonic where the tune is 99·9% likely to end. You play the dom7, & sit back expecting the tonic to follow as surely as night follows day...