You can assume in this world there exists as part of its natural phenomena the so-called "vital force". This is a completely repudiated scientific concept devised when our understanding was less developed. A person with the ability to transfer the vital force from other living creatures would resemble your life-feeder.
There's no reason why, in this case, you couldn't postulate that vital force can drawn off from another organism almost like electricity. It might even be possible to develop a technology to transfer vital force in this world. Thus providing technological vampirism to extend the lives of the rich and powerful. Or even reanimate creatures constructed from human and animal parts like good old Victor Frankenstein.
This does mean biology in your fictional world will be more than somewhat different from that in ours. The vital force concept was a real idea. History and the March of Science has totally repudiated its validity, now it's just bad pseudoscience, but there's no reason it couldn't be used in a fictional world.