There is an inspiration lineage from Dremel, but there are also very substantial differences. Dremel handles nested data, but doesn't like variable schema and tends to generate code early (AFAIK). Drill handles data that changes shape and type and generates code very late.
The idea that SQL can be applied to data that is pretty different from traditional relational data is definitely common between the two.
The idea that SQL can be applied to data that is pretty different from traditional relational data is definitely common between the two.