Why is "LGS" the standard term for a game store?
"Local" implies familiarity, and some connection specifically to you. It's a store near you, it's convenient for you, it's something from your area that you can be proud of, it's part of your community, it's a place you might see people you know. It also implies that it's not a chain. All of this adds up to a more warm and fuzzy emotional connection.

Brick and mortar, on the other hand, is really just about offline vs online. A brick and mortar store could still be a giant national big box chain store. The only important thing is that it's physical, so it still sounds pretty impersonal.

Note that this isn't just a gaming thing; for example LBS (local bike store/shop) is pretty common too.

You can also see a lot of other common "local * store" terms in the Google ngram viewer. "Local grocery store" is the most common, tying into the local food movement.