The episode serves more functions than that.
We know that by Breaking Bad Stacey is keeping Mike at a distance. This is showing that fracture’s start.
It is also the insight into Mike’s psyche. Established in visual metaphor that Matty’s memory (and likely his sense of guilt) is fixed in cement for Mike. Stacey’s comment about being able to not think about Matty as constantly, not having his memory in the same cement that Mike does, (even if feeling guilty and even scared about that) is psychological attack on that. Mike’s go-to defense mechanism, his coping strategy, is “intellectualization”. He uses going to reasoning, his professional skill set, to “block confrontation with an unconscious conflict and its associated emotional stress.” He thinks to avoid having to deal with his feelings. And he punched down liar guy to displace his anger at Stacy beginning to move on and put grief in a box rather than front and center all the time.
It is why he is not capable of just sitting around watching ballgames and cashing the checks. He needs to be keeping his mind working in his professional reasoning capacity.
This is what drives him as a character.
There is a parallel I think to Walt. Mike ends up saving lots of money for his granddaughter and likely convinces himself that doing that is why he does the unsavory things he does, just as Walt tries to think of himself as doing it for his family. But we as viewers know better. They are not really doing what they do to provide or for the money. Neither of them.
Liar guy was lying. Maybe for good psychological reason maybe not. Certainly if his attacking liar guy causes harm the fracture with Stacy will accelerate. Minimally it has walled Mike off from furthering his friendship and possible budding romantic relationship with breakfast woman.
It also creates a parallel with Jimmy. Both have a hard time tolerating people who can be scammed. Mike attacked the scammer more than the chumps and Jimmy the chump, but they both have some contempt for the gullible.