OK, well sorta. Good news is that "immunity" on an individual scale isn't super duper important. The paper didn't measure the body's response to a reinfection, which is probably more important. Most/all infections have decreasing antibody titers over time, just a question of how long. So basically, you can get reinfected (have the virus circulating in the body), but the body will ramp up a response much more quickly than during the initial infection. So you might not show symptoms even if infected, and the symptoms are probably milder even if reinfected. This is super good news, as some viruses cause a hyperimmune response on reinfection, causing worse symptoms than the initial infection.
What's the upshot?
--Herd immunity isn't likely to happen if these results hold. That's because the virus can still circulate within the community
--We're going to potentially have a hard time determining who's been infected. Public health repercussions because again, if there have been a bunch of infections that we don't know about, the mortality and hospitalizations will be less than expected as people mount a quick response the second time around.
--You'll probably need frequent booster shots of a vaccine. I have certainly counted on this assuming that the virus will mutate, but this would be another reason.
I'm guessing that eventually this is going to act like the seasonal flu and follow the trajectory of the spanish flu. Hopefully we can short circuit the massive number of deaths by getting a vaccine sooner rather than later.
Damn that's a long response. You can always tell when I'm at a computer v. a phone...