Sentiment analysis is descriptive, not predictive
Sentiment analysis is descriptive, not predictive (as long as it describes the current, general sentiment related a topic - predicting future sentiment based on past sentiment and potentially other factors would be predictive).
Analyses are exact or probabilistic. Predictive analysis is generally probabilistic because we rarely know the future for sure.
Most descriptive analyses are exact (number of likes, number of clicks, Klout score, S&P index, etc.) because they are defined by a single, deterministic method or a single authority, which does not allow contradicting results.
Sentiment analysis is a probabilistic descriptive analysis because it attempts to measure something and fails to measure it exactly. Sentiment analysis generally attempts to measure the ratio of positive vs. negative sentiment related to a topic in a given corpus. It is based on natural language processing, which is typically not perfectly accurate.