Tim Chow's proof that the moser-number is much smaller than grahams number

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The link here shows a proof from Tim Chow that the moser-number is much smaller than grahams number.

I do not understand the inequality

3^^...^^3 (3^^^^^3×2-1 arrows) << G 2

What does G 2 mean here ?

If the sequence

$$G_1 = 3\uparrow^4 3$$

$$G_{n+1} = 3 \uparrow ^{G_n} 3$$

for all $n \ge 1$

is meant, I understand that the left number is much smaller then $G_3$, but I do not understand that it must be smaller than $G_2$.

What am I missing here ?