The extent to which learners benefit from instruction may be largely dependent on their individual abilities. However, there is relatively little work on the interaction between instructional effectiveness in second language learning and learner individual factors. In this study, we investigated the relationship between instruction, individual differences in cognitive abilities (working memory and declarative memory), and second language vocabulary acquisition in the context of web-based intelligent computer assisted language learning (ICALL). To this end, 127 adult learners of English, predominantly advanced-level, German-speaking learners, read news texts on the web for about two weeks using an ICALL system under two instructional conditions: form-focused and meaning-focused instruction. Learners in the form-focused condition read and completed automatically-generated multiple-choice gaps where phrasal verbs appeared in the text, while learners in the meaning-focused condition simply read and did not complete any gaps. Mixed-effects regression analyses showed that working memory was associated with vocabulary acquisition and that this association depended on the instructional context, with working memory being predictive of learning only in the form-focused condition, suggesting an aptitude-treatment interaction. Furthermore, declarative memory abilities were related to learning only as measured by the Continuous Visual Memory Task, and the relationship was not moderated by instructional condition. Overall, the study contributes to accounting for variability in second language learning in general, as well as in instructional contexts supported by intelligent CALL.