The way you described the device, it is already incapable of fulfilling its main purpose, so subverting is kind of moot.
You didn't mention how it detects who should get the kill. So if people travel in groups, everyone in the group will get a point whenever a single person makes a kill. You could just attend a lot of executions, and come early so you can have a front row seat, to rack up the points.
You didn't account for causality, so people dying accidentally near you would increase your score. A sniper or poisoner would fail to be awarded their actual kills. In fact, friends of the sniper's victims would end up kill-stealing from the sniper. The laziest approach here is to just hang out in an emergency room. Especially being around people who get resuscitated a few times is great, you get multiple kills from each person. Being a journalist following people on suicide missions is also another "easy" one.
You haven't explained in detail how the device senses lifesigns, but most likely there is at least one material that blocks it (if it relies on electric fields, those are blocked with Faraday cages). You just make a box out of that material and have your friend go in and out of it repeatedly, and each one would be a "kill".
As described, the device also awards a kill every time someone leaves its detection radius. So a racecar driver will score a kill for every spectator at every lap. Flying a plane or helicopter at low altitude (eg. above a busy highway) will have similar effects, as would just standing at an airport where passenger planes take off. Or you could find a big cruises ship and just keep stepping in and out of the detection radius. Even walking through a dense city center should do it. My bad - you did say "without leaving its detection radius".
Of course the obvious solution is to just hack the device and overwrite the memory.