The information is only a few hours/days old. If the radiation were strong enough to produce casualties that fast, it could probably be detected by aircraft, maybe even satellites. That's about like walking into an operating nuclear reactor, or having a mass of nuclear material go supercritical in front of you (you'd know, you'd see the pretty blue flash).
That indicates that most of the radiation is probably not beta or gamma radiation, but alpha radiation,
That indicates no such thing, just that the radiation is at most only a few rads* -- thousands of times what is considered safe, but hardly instantly lethal (650 rads will kill 50% of those exposed within 30 days; a medical x-ray is measured in a few thousandths of a rad)
plutonium-239's calling card.
Also the calling card of numerous other isotopes.
Since the people who discovered the radiation at Al Tuwaitha have reported no health problems,
Yet. But see also above on dosage.
the plutonium is most likely purified -- and therefore usable in a weapons program.
That much plutonium would be quite thermally hot (as the alphas from anwhere but the surface of the plutonium get absorbed and the energy converted to heat). If there's really that much of it, it sounds like it'd be at or above critical mass and spontaneously fissioning from random neutrons.
This report sure extrapolates a lot from a lack of data. Don't buy it, wait for the test results.
(* Note for the pedants: I'm using rads, rems, roentgens, seiverts, and all those other radiation units as roughly equivalent, although I know it really depends on whether you're talking about ionizing potential, absorbed dose, biological effect, et bloody cetera.)