I'd probably reframe your question to be slightly broader, such as "why do vocabulary tests correlate so highly with estimates of general intelligence (i.e., g)?".
Anyway, here a few thoughts:
- Verbal ability measures, including vocabulary tests, are often part of IQ tests. Thus, some of the correlation may flow from our conceptualisation of intelligence as requiring verbal aptitude.
- Ability tests tend to intercorrelate; these correlations are generally greater within a domain (e.g., verbal, spatial, etc.), but even across domains, correlations are observed. Thus, whatever drives correlations between any ability test and general intelligence may also partially explain the vocabulary-IQ correlation. However, this isn't the complete story, because certain tests (from memory, e.g., Raven's Progressive Matrices and Vocab) correlate more with g than others.
- People with greater intelligence may be more likely to seek out verbal stimuli, be provided with verbal stimuli, and retain and understand verbal stimuli, all processes which over many years would accumulate into a greater vocabulary. Similarly perhaps, relatively stable environmental factors might simultaneously increase intelligence and vocabulary.
I'd be keen to read any specific studies which involved a vocabulary based intervention and see whether (a) this was successful in increasing vocabulary test scores, and (b) whether the intervention lowered the correlation with vocabulary and intelligence.