2.9The dominant is always degree 5

In C:

1 = C

5 = G

So:

G → C

is 5 → 1.

In G:

1 = G

5 = D

So:

D → G

is 5 → 1.

In D:

1 = D

5 = A

So:

A → D

is 5 → 1.

This already explains:

G7 → C

D7 → G

A7 → D

E7 → A

which you saw on the chord chart.

They are not four unrelated facts.

They are all:

V7 → I