Diastatic malt extract is simply malt extract still containing enzymes capable of converting starches to sugars. As diastase enyzmes are rapidly denatured by heat, the overwhelming majority of malt extracts are not diastatic. Using diastatic malt extract permits a certain amount of mash-like conversion to take place without the hassle of mashing.
Edme is the only company of which I am aware which makes a brewing-quality diastatic malt syrup. Unfortunately, I don't think it's really available in the US, though UK homebrew suppliers seem to stock it.
In this recipe, I suspect the intent is to use diastatic extract to convert the starches in flaked barley to fermentable sugars. This is absolutely necessary with Dry Irish and Oatmeal Stouts, as the unmalted adjuncts (flaked barley and flaked oats) cannot be used effectively in extract-and-steep techniques. Steeping flaked grains adds nothing but haze, foam-killing oils, and glop; they must be mashed to have any effectiveness at all.
Cheers,
Bob