How to express the concept of "the degree of excitement" in one word?
Degree of excitement is the most precise way to put it. However, in psychology research [1], when measuring excitement quantitatively on a scale, the terms excitement and arousal can be used to label that type of measurement.
If that does not fit your purpose, and you still need a "single-word" label (perhaps for word count purposes), you could use excitement-level, but this is a bit sneaky.
Source: Spielberger, C. (2004). Encyclopedia of applied psychology. Academic press.