I have a couple of 100 watt laser cutters. They cut 3/16" plywood really nicely - and 1/2" plywood with difficulty...providing they are properly cleaned and focussed and cutting at around 2000mm/minute. A 2 watt laser...well, draw your own conclusions. There is no magic going on. To cut wood that thick, it has to move VERY slowly and probably make multiple cut passes.
The Blu-ray laser approach *IS* great for thin materials though. 1/16" balsa, paper, cloth, that kind of thing. So this is a useful contraption - I just wish they wouldn't over-sell it...it's just not that good.