(1) Since $a=2$, we have $A=\{x | 2 \leq x < 4\}$, $B=\{x | 3x - 7 \geq 8 - 2x\}=\{x | x \geq 3\}$.
Therefore, $A \cap B=\{x | 3 \leq x < 4\}$, $(\complement_{\mathbb{R}}A) \cup (\complement_{\mathbb{R}}B)=\{x | x < 3 \text{ or } x \geq 4\}$;
(2) Since $A \cap B = A$, it implies $A \subseteq B$,
thus $a \geq 3$.

The final answers are:
(1) $A \cap B=\boxed{\{x | 3 \leq x < 4\}}$, $(\complement_{\mathbb{R}}A) \cup (\complement_{\mathbb{R}}B)=\boxed{\{x | x < 3 \text{ or } x \geq 4\}}$;
(2) The range of values for $a$ is $\boxed{a \geq 3}$.