I might be misreading their algorithm, but from my look at the paper the key improvement is a non-uniform strategy where they divide the array into buckets and

I might be misreading their algorithm, but from my look at the paper the key improvement is a non-uniform strategy where they divide the array into buckets and focus on different buckets as they fill the table. This increases the average number of locations to be probed even when the table is emptier. They still place the item in the first empty slot they see with this strategy. The "skipping slots" has to do with jumping ahead in the hash sequence.