You cannot side load Play store. It will always crash. It requires flashing gapps.zip via a custom recovery like ClockWorkMod or TWRP. Mach Speed Trios are generic models which come pre-rooted (and don't need a SU app for some reason) but do not support Play. I am not sure if there is even a custom recovery since devs don't really mess with these tablets. There are alternatives like Amazon Apps and 1Mobile, SlideMe as well
I've not recommended this in the past. But I've actually downloaded a few apps and games from 1Mobile in the last couple of days. Because Play's frequent "This app is not available in your country." and "This app is not compatible with your device." nonsense was really starting to annoy me.
Using a Chinese app store in China....oh well.
I often use SlideMe and GetJar as well. 
)and then I'll nab the apk.