might be missing something here, but re the step's scale: the value shows as 1.215 but each repeated stair is incrementally smaller - how come? shouldn't the repeated action keep increasing the size?
When you use the Object offset, what's happening is that Blender is going to use the relation between your original object and your Empty as a "first step" mesure.
In other words, your Empty equals your first array copy.
So in this case if you scale the original object and leave the Empty as default, your Empty is smaller than the origin object therefor it means that your first array step is smaller and as you go further in the array, you keep applying the ratio transform that there is from the origin-object to the Empty and you end up going smaller and smaller.
Hope this explanation is clear ^^'
The size of the duplicate instance is worked out by the modifier reference objects scale(in the example the empty) divided by the active/modified objects scale (in the example the step) times the previous objects size. So at the point in the video you're referring to the empty was set to scale of 1 - so when increasing the object to 1.215 the duplicates where 1 / 1.215 of the previous, meaning they got smaller. This is why keeping the original object scale set to 1 makes it easier as then there is no division to complicate things and the changes in size come directly from the empty scale values.
