Well it is the same exact Enlightenment as in other schools, just expressed differently.
Kami are the spirits or energies of the universe. These are things of the same nature as devas and maras of Pali Canon and deities of Vajrayana and Shingon. In Greek paganism they were called daemons. Jung called them complexes. In our times we could call them memes.
Because in Theravada and more so in Yogacara the world is made out of phenomena of mind, external entities having their own existence are not posited. Still, what animalistic schools would call "mastery of spirits" is practiced in phenomenological schools as "mastery of phenomena".
When seen at universal scale, kami are made out of Musubi, the creative power permeating the universe, which refers to the same principle that is invoked by the concepts of Mahavairocana of Shingon, Tao of Taoism, Buddha Nature of Mahayana, Shunyata of Madhyamaka, Three Marks of Existence of Theravada, Dang energy of Nyingma and so on.
As the goal of Shingon is the realization of one's nature as identical with Mahavairocana, and the goal of Taoism is unity with Tao -- the goal of Shugendo is becoming one with kami.
This should not be understood primitively, as expanding one's "I" to the size of the universe (an interpretation sharply criticized by Gotama), but rather, as deconstructing "I" completely and practically, while attaining effective insight into one's own nature being an interplay of formations.
The naive experience of non-duality ("I am the universe"), which is sometimes mistakenly equated with bodhi, is what Buddha called “the state of Brahma”. It is just one of the experiences that practitioner has along the way, and may both happen before bodhi and be intentionally generated after bodhi. In addition to the state of Brahma, Buddha enumerates the following liberation-related states (AN 4.190):
The state of a deva — ability to intentionally generate rapture, pleasure, bliss, and equanimity in one’s body-mind at one of the four jhana levels.
The state of Brahma – development of loving-kindness (really, the four immeasurables) culminating in the experience of unity with the world.
The state of imperturbability — ability to maintain one of the four formless absorptions.
The state of an arya ("noble" / "civilized") — the state of having first-hand experience and direct realization of the validity of the four noble truths, the principle of this/that conditionality, and the three marks of existence. More broadly, the state of arya entails deep understanding of practical implications (benefits, drawbacks and limitations) of any conceptual construct, as well as the virtual nature (aka "shunyata") of all modes of phenomenal existence.