At this point in time specifically, a $1000 laptop (the comparable general purpose option) is going to be a mid-to-upper entry-level one. Because it's supposed to be general purpose, it won't have hardware chosen to maximize gaming potential. Likely all of these options would only allow a RAM or hard drive upgrade, as well. This puts them upon somewhat equal footing with the Steam Machine, except I would hazard a guess that the Steam Machine would still do better at gaming due to the hardware selection they had available at production time.

And if you mean building a $1000 gaming Linux box, good luck not going over that limit with current RAM, GPU, and SSD prices.