duōbus puerīs = one of
the two boys
The ablative is because ē/ex always takes the ablative. (For future reference, you will also see dē used this way, also with the ablative. There is no difference in nuance or meaning that I know of.)
I would have expected Alter puer valet, alter aegrotat.
This is valid too, but the grammatical role of 'alter' and 'puer' differs between the two. In your sentence, 'alter' is an adjective modifying the subject, 'puer'. In Orberg's sentence, 'alter' is (acting as) a noun, and puerīs is the object of ē.
See the difference?