Installing a ceiling light with screw holes that don't match the ceiling bracket
You need to acquire a light fixture mounting bracket. The type that you need would look like the bracket as shown in the picture below:



Install it through the longer slotted holes into the existing electrical box holes. You can use the screws from the old light fixture.

Due to the deep recess of the electrical box the bracket arm with the long slotted holes will reset against the ceiling drywall. The other arm needs to be oriented so that the ends project down from the ceiling so that there is clearance for the screws from the light fixture to go into the threaded hole but not have to enter the ceiling surface. This picture will help to show the mounting strategy:

 

The new fixture then can mount into one of the sets of threaded holes in the other arm of the bracket.