Promissory estoppel sounds in equity, not tort. The theory of recovery is simply "estoppel" - the promissor will be held to the promise, the cost of cover, and potentially to the consequential damage for breach of the promise. The person who broke the promise is the "promissor" and the injured person is the "promissee," or more often something else entirely, unrelated to the cause.
Anyhow, your question appears to ask for the adjective one might apply to the promissor. I'm not sure I have seen anything standard in this regard, and the language can be as colorful as the parties or court like. A breach of promise is treated like a breach of contract, so any adjective one applies to a misfeasant breaching contract party one might also apply to a misfeasant breaching promissor. I think "breaching" is probably the answer - as in, "I'm suing a breaching promissor for inequitably breaching his promise!" Doesn't sing quite like "tortious" and "negligent" due, I'm afraid.