As far as I'm aware, hordenine is not a banned substance for the military. I don't even believe it is a banned substance by the anti-doping agency. Hordenine is a component of many different kinds of plants, most notably, barley.
Hordenine is considered a sympathomimetic type supplement meaning that it stimulates the sympathetic nervous system. It mimics many actions of our naturally occurring neurotransmitters such as epinephrine and dopamine. Sympathomimetics have a variety of uses including a feeling of energy/explosiveness, heightened alertness, increased metabolism etc...
Again, hordenine is a naturally occurring substance that many people consume in small amount from their normal diet. Recently, it has been isolated and touted as a work out or weight loss aid.While the benefits for this use aren't well studied, hordenine appears to be fairly safe and well tolerated. I should mentioned however that according to some research, hordenine, may yield false positive results on tests fos for various opiate drugs. This doesn't appear to be common however.
DMAA was a synthetic drug that was invented and manufactured by the drug company Eli Lilly. Over time, it was realized that the drug when used for recreational and supplemental purposed, was fairly unsafe and was thus discontinued. Hordenine may not be quite as effective, but it appears to be much safer.