I use leveling quite often and combine this with priorities.
After playing around with the file you set up, I conclude that the delay field allows you (as the planner) to specify a late start of a resource assigned to a particular task. Leveling will not change that value and will basically respect the delay and plan around it. It allows you to plan a staggered start for multiple resources assigned to one task.
Leveling delay is the delay that occurs within a task if due to leveling one of the assigned resources cannot start at the same time as the earliest starting resource assigned to that task. You can see this by adding the priority column (in the Gantt view) and changing the priority for T2 to 540 and level (use leveling order Priority, Standard to see the effect). This will force R1 to work on T2 first before continuing on T1. R2 will start on T1 immediately however, so R1 is causing a delay in T1. When all assigned resources are starting at the same time and work continuously no leveling delay is shown, even though the complete task may be delayed due to leveling.
Inserting question. It may have put me on a solution for some problems I occasionally encounter working with leveled schedules.