Hi Buck,
This happens because the RuleID is of Long type (i.e., integer). The text you see in the field (Rule_1 etc) is a coded value which is stored on the geodatabase level (right-click the geodatabase in Catalog and choose Properties > Domains tab).
If you want to calculate the "Rule_x" in the newly created field, I'd suggest using the Field Calculator like you do now and get the digits (1,2,3 etc) and then calculate the field by adding the "Rule_" again by using the using the Field Calculator.