Should events be classified as tangible or intangible? Maybe.
If tangible ("concrete") and intangible ("abstract") nouns existed, their should be some linguistic test where the answer would separate words into these two categories. According to the introduction to a paper titled "Abstract and Concrete Sentences, Embodiment and Languages" (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3173827/),
Nelson and Schreiber (1992) and Wiemer-Hastings et al. (2001) asked people to judge the concreteness of large sets of words; they found a bimodal distribution (according to features, such as tangibility or visibility), not a dichotomy. Things are even more complicated when words are embedded within contexts. Most of us would agree that the noun “apple” and the verb “to grasp” are concrete, but judging verb–noun pairs such as “to grasp the meaning,” or “to think about an apple” (e.g., Aziz-Zadeh et al., 2006) is all but simple. In addition, the meaning of a sentence is often influenced by a specific language and culture; furthermore, it has been shown that this linguistic and cultural influence is particularly strong for abstract compared to concrete words (Boroditsky, 2003).
When linguistic tests are run on native speakers, the results are mixed within a language community (perhaps indicating that the categories are not really a part of the shared grammar of the linguistic community), vary across cultures and linguistic structures, and change depending on linguistic context ("an apple" vs. "to think about an apple"). The paper goes on to discuss and advance theories which attempt to correlate the huge variety in interpretation of tangible/intangible nouns to biological systems (e.g. brain functioning, the visual system, etc.).
You have stumbled across an active area of research for some linguistics. If you are interested in responding to or implementing your own theories on the subject, I found googling "abstract" vs. "concrete" nouns to be a good starting point.