Without digging into the soil, the radiation in the Red Forest is upwards of 10.0 mSv/hour, which is .01 Gy/hour, and would hit 3 Gy in just about 12 days, which is sort of the baseline for major health concerns.
Merck has a huge document based on radiation sickness and how much radiation a person can typically withstand.
By comparison, the average person in the US gets 3 mSv/year. So in some places in the Red Forest, you're getting more radiation in an hour than the average American does all year. On an average flight, you get roughly .0001 mSv/hour.
So if we account for things like digging into the soil, the number of dust particles that were kicked up while digging, and the fact that everything the soldiers were touching, eating, and drinking were covered with radioactive material it's not surprising that some soldiers are already starting to die due to exposure.
Here's the breakdown of what happens based on
how many Gy a person absorbs (some medical images, so take that as a warning).
Anything more than 8 Gy pretty much means you're fate is sealed with or without care. Anything under 2 Gy means you have a decent chance to survive and from that baseline up to the 8 Gy number, the chance of death rapidly increases.
Given how quickly the soldiers died, they could've easily received upwards of 30 Gy. This is assuming they're a healthy adult with no underlying conditions either.