The ordinary version is real, the distance version is not shown
Psychic empathy
Psychic empathy is the claimed ability of feeling other people's emotions directly, at a distance or without cues. It has been tested — Emotional contagion research — Hatfield, Cacioppo and Rapson, 1993 onward. Emotional contagion is real and well established. It works through ordinary perception — face, voice, posture, breathing — and disappears when those channels are removed.
The experiment
Emotional contagion research — Hatfield, Cacioppo and Rapson, 1993 onward
This is the ability most worth separating carefully. People who describe themselves as empaths are usually describing something genuine and measurable. The disputed part is only whether it works without the senses.
Where the word comes from
The word entered English in 1909 as a translation of the German Einfühlung — from aesthetics, not from the occult.
Terms in this field are younger than they sound. Most were coined between 1840 and 1930, in the Spiritualist and Theosophical revivals, and then presented as ancient. Dating them is the cheapest reality check available.