What constitutes an emotional disorder? Watson, et al. (2008) states that a superclass of mood and anxiety disorders should be given a nonspecific label, such as ‘emotional disorders’.
They stated that this superclass

can be decomposed into three subclasses: the distress disorders (major depression, dysthymic disorder, generalized anxiety disorder, posttraumatic stress disorder), the fear disorders (panic disorder, agoraphobia, social phobia, specific phobia), and the bipolar disorders (bipolar I, bipolar II, cyclothymia).

There have been different remits put forward in Neurophysiology, Psychology and Psychopathology journals to define what constitutes an emotional disorder.
Goldberg, et al. (2009) says they include:

generalized anxiety disorder (GAD), unipolar depression, panic disorder, phobic disorders, obsessional states, dysthymic disorders, post‐traumatic stress disorder (PTSD) and somatoform disorders. We have also included neurasthaenia, as this diagnosis is commonly made in many parts of the world, and is in the ICD‐10. We have preferred the term ‘emotional’ because we include somatoform disorders in the group.

yet, Baek (2014) says:

Typical emotional disorders are anxiety disorder, depression, and bipolar disorder

Sung, et al. (2016) pointed out that

The term ‘emotional disorders’ is not a clearly defined medical term, but is commonly used to refer to psychological disorders (e.g., generalized anxiety disorders and major depressive disorders) that appear to affect the emotions. ‘Emotional disorders’ in this study refers to the symptoms of anxiety and depression

Where there are moves to improve the diagnostic procedures for mental disorders through systems such as HiTOP (Stony Brook Medicine, 2017; Kotov, et al., 2017) — see also my answer to How does a person know if he should seek treatment for depression since feeling moody is unavoidable? — has there been any attempt since 2016 to put together definitive criteria to determine what constitutes an emotional disorder?
References
Baek, S. B. (2014). Psychiatric rehabilitation of emotional disorders. Journal of Exercise Rehabilitation, 10, 205–208. 10.12965/jer.140143
Goldberg, D. P., Krueger, R. F., Andrews, G., &amp; Hobbs, M. J. (2009). Emotional disorders: Cluster 4 of the proposed meta-structure for DSM-V and ICD-11. Psychological Medicine, 39, 2043–2059. 10.1017/S0033291709990298
Kotov, R. et al., 2017. The Hierarchical Taxonomy of Psychopathology (HiTOP): A dimensional alternative to traditional nosologies. Journal of Abnormal Psychology, 126(4), pp. 454-477. doi: 10.1037/abn0000258
Stony Brook Medicine (2017). The Hierarchical Taxonomy Of Psychopathology (HiTOP). [Online]
Available at: https://medicine.stonybrookmedicine.edu/HITOP/publications
Sung, C. W., Chen, K. Y., Chiang, Y. H., Chiu, W. T., Ou, J. C., Lee, H. C., ... Wang, J. Y. (2016). Heart rate variability and serum level of insulin-like growth factor-1 are correlated with symptoms of emotional disorders in patients suffering a mild traumatic brain injury. Clinical Neurophysiology, 127, 1629–1638. 10.1016/j.clinph.2015.08.006
Watson, D., O'Hara, M. W., &amp; Stuart, S. (2008). Hierarchical structures of affect and psychopathology and their implications for the classification of emotional disorders. Depression and Anxiety, 25(4), 282–288. 10.1002/da.20496
Bullis, at al. (2019) tackled this very question this month, and outlined criteria to determine what an emotional disorder is:

The disorder is characterised by the experience of frequent and intense negative emotions;
There is an aversive reaction to the emotional experience itself that is driven by the individual's diminished sense of control and negative appraisal of the emotion; and
The individual engages in efforts to dampen, escape, or avoid the emotional experience, either preemptively or in reaction to the onset of a negative emotional state.

The paper also expands on each of the criteria and pointed out in the summary that

these criteria would only be considered an emotional disorder if the associated distress and functional impairment were chronic and significant. [emphasis mine]

The term chronic is well defined within the fields of medicine and mental health, but the question now arises as to how significant is significant in order to say that the criteria can be considered?
References
Bullis, J. R., Boettcher, H., Sauer‐Zavala, S., &amp; Barlow, D. H. (2019). What is an emotional disorder? A transdiagnostic mechanistic definition with implications for assessment, treatment, and prevention. Clinical Psychology: Science and Practice, e12278. doi: 10.1111/cpsp.12278