Next challenge: do the same thing with maple or another type of stained wood veneer. I think the Varmint Evolution rifle uses this technique and looks awesome. Reminds me of skateboards, pretty much the same technique.
You're right, this is just lamination, no matter if it's with wood, fabric or paper. In fact, since I've been REALLY considering getting some checkering tools lately, so I've been thinking about doing this same thing with heavy paper.
I'm not sure the fabric/canvas micarta is the best to try to checker but I'll bet the paper would be fine.