In my (superficial) explorations of different traditions, I discovered that the general category that diksha falls under is called shaktipat, a transfer of energy which facilitates awakening.
It is used systematically, by many teachers, in the Indian traditions, and probably more or less systematically, sometimes even accidentally, by some teachers in many other traditions.
Shakti means energy and pat means touch, and it seems to typically be done through touch, by laying on of hands or even hugging (Amma), but it can also be transfered through gazing or even at a distance - either through an intentional transfer from the giver, or through intention and prayer from the recipient's side.
Shaktipat and energy healing
There are of course several parallels between this and the (in the west) more familiar faith/energy healing.
In both cases, the "giver" functions as a catalyst for the energy (channeling or awakening it), and the energy itself functions as a catalyst for either healing or awakening. The energy works on and in the energy field of the recipient, allowing the physical and/or consciousness aspects to reorganize. Where energy healing facilitates healing, shaktipat facilitates awakening.
What does seem somewhat new in diksha is its predictability and universality. It seems that just about anyone can go through the three week process to become a diksha giver, and that the process unfolds in generally the same way for the recipients, up until awakening to realized selflessness.
From what I hear, and experience myself, it also seems that the different diksha givers transmit their own flavor of the diksha, emphasizing different aspects of the awakening process (for instance endarkenment.)
Muktananda and Adi Da are known for their use of shaktipat, and it is also an important element in Waking Down (not surprisingly, since Saniel Bonder was a student of Adi Da.)
Amma seem to transfer a heart-awakening shaktipat through hugs.
There is a possibility that some Christians do something similar through laying on of hands, although I am not sure about that.
The Tibetans probably have it in their repertoire as well, as they seem to have a very comprehensive and inclusive toolbox.
And, as mentioned, some teachers in any tradition probably use it, either accidentally or more intentionally. Sometimes even by just being in the same room as their students.
Especially in the west, there is a natural and healthy skepticism about both shaktipat and energy healing, and the only way to get some more clarity around it is to put it to the test through scientific studies (double-blind, using physiologically and psychological measures of changes) and also by trying it out personally.
It is also interesting to look at the different factors involved. Some of the effect does seem to be through the energy transfer, allowing the energy aspect of the recipient to change which in turn invites the physical and/or consciousness aspects to shift. The other aspects certainly include the expectation and receptivity of the recipient, which in itself can allow for significant shifts.