That doesn't mean the boars are radioactive.
They test as radioactive because they've eaten plant material contaminated with cesium-135 and/or cesium-137. What's testing as radioactive is the cesium within them, not the flesh of the hogs. And most of that contamination (estimates are as high as 68%) is cesium-135 that was fall-out from Cold War weapons testing, not the Chernobyl accident.
Animal tissue can become radioactive but if it does -- strictly speaking -- it won't remain living for very long, because it takes several times more than a lethal dose to make it so. So inside of days or weeks of having been made radioactive, it would cease to be living.
This gets distorted a lot because people mistakenly believe that radioactivity is contagious, and it is not. You can't be made radioactive simply by contact with something that's already radioactive. There's more detailed information here but, in a nutshell, to "become irradiated," non-radioactive material has to absorb A VAST NUMBER of neutrons emitted by a decaying radioactive isotope.
The VAST NUMBER bit is important in this case because the only way to get that intense a dose is from a sustained nuclear reaction, and the two most likely sources for that are nuclear reactors or nuclear bombs.
So for those boars themselves well and truly to have been radioactive, they would have had to have been at Chernobyl on that day 40 years ago, and been exposed to the reactor itself, not merely the fall-out. And then they would have had to survive 40 years after receiving a several times lethal dose of radiation.
Strictly speaking, not possible.
No it doesn’t mean the boars are radiated but since boars don’t know about borders well.....