The term “a memory gets stuck in the amygdala due to too much LTP between neurons” is a metaphoric or heuristic statement that was utilized a great deal in the middle to late 90s. From more recent research we now know that memories are not contained in any one part of the brain, but rather are stored in fragmented forms in the various distributed neural networks that were active when the event (to be remembered) was first encoded. It appears that the Engram (the neural map of the various distributed sites containing the fragments of information that was processed during the encoding of the experience and which requires reactivation in order to produce the experience of remembering something) is mediated in the hippocampus and para-hippocampal regions.
While the limbic system, and the amygdala within it, are certainly very important brain areas when it comes to our experience of emotions, neuroscientific research makes it clear that our emotionality is not restricted to these areas alone. Richard Davidson’s research has demonstrated that the right frontal lobe of the brain is highly involved in distressed emotion (Davidson & Begley 2012), and evidence provided by Panksepp & Biven (2012) makes it clear that areas of the brainstem are also highly important. In fact, Panksepp states that, “we know from neuroanatomy that the most important area for emotions is not the amygdala, as some people have marketed, but it is in the mid-brain, at the very core of the brain area called periaqueductal gray, because that’s where we get emotional behaviors at the lowest amount of electricity for deep brain stimulation.” (2012). Panksepp & Biven (2012) discuss the neurological fear circuit, which includes the periaqueductal gray, in addition to the amygdala, as well as the frontal lobes.
Information processing/consciousness (sensation, perception, cognition, memory, emotion, and somatosensory integration) are mediated by neural linkage and neural temporal binding When memory is accessed adaptively, it is linked with emotional, cognitive, somato-sensorial and semantic networks which facilitate its accuracy and appropriateness with respect to time, place and contextual situation. When processed traumatically, or under fearful circumstances, experiences appearto be encoded, but unlinked to existing neural networks. Pathology/PTSD results when the linkage/binding systems in the information processing system are impaired. Therefore, experiences are inadequately processed and unlinked to somatosensory, cognitive , emotional and memorial networks, thereby becoming susceptible to inappropriate access and experienced in fragmented form, with respect to time, place and context. This phenomenon of PTSD is what used to get characterized as “memory stuck in the amygdala” prior to our current understanding of neural linkage and binding.
The exact mechanisms of EMDR’s amelioration of PTSD symptoms is not as yet known. What appears to be clear from the outside, is that it appears to mediate the following: desensitization/depotentiation of fear circuits (encompassing areas of the brainstem, midbrain and limbic areas, anterior cingulate gyrus, and orbitofrontal cortex); and the facilitation of neural linkage of somatosensory, cognitive , emotional and memorial networks and the temporal binding of these areas.
Just exactly how bilateral sensory stimulation, combined with clinical procedures, accomplishes all of this is yet to be inferred empirically. The article referenced in your question attempts to explain the desensitization/depotentiation, utilizing data from a qEEG examination of EMDR.