Identifying auditory attention by comparing auditory stimuli and corresponding brain responses, is known as auditory attention decoding (AAD). The majority of AAD algorithms utilize the so-called envelope entrainment mechanism, whereby auditory attention is identified by how the envelope of the auditory stream drives variation in the electroencephalography (EEG) signal. However, neural processing can also be decoded based on endogenous cognitive responses, in this case, neural responses evoked by attention to specific words in a speech stream. This approach is largely unexplored in the field of AAD but leads to a single-word auditory attention decoding problem in which an epoch of an EEG signal timed to a specific word is labeled as attended or unattended. This paper presents a deep learning approach, based on EEGNet, to address this challenge. We conducted a subject-independent evaluation on an event-based AAD dataset with three different paradigms: word category oddball, word category with competing speakers, and competing speech streams with targets. The results demonstrate that the adapted model is capable of exploiting cognitive-related spatiotemporal EEG features and achieving at least 58% accuracy on the most realistic competing paradigm for the unseen subjects. To our knowledge, this is the first study dealing with this problem.