Lego is the brand name; "let's play with Lego" is short for "let's play with the Lego bricks". I think it's much closer to a group noun :)
See also: Meccano, Duplo, Brio, Scalextric.
LEGO(tm) brand bricks
In Germany we even stopped pretending that it's just a bunch of bricks and use the word as if it were the name of the game. We say "Let's play Lego". Does this sound strange in English?
You mean "not in the US"? Im not sure exactly, but only have heard people in US saying "Legos". (Australia here, we play with Lego!)
Totally opaque to whether that's "lego's" or "legos" and children in general probably don't care for an overzealous syntactic classification of single morphemes either.
Is "gimme the lego over there" strange? I think it is, and if it is, then it's an interesting dater point to support this hypothesis.