The phrase is definitely correct idiomatic usage.
To make a case for something, when something is a noun (or pronoun), is to provide good reasons why the named thing should be considered for use at whatever tasks that thing is normally used for.
You could consider it to be a shortened form of make a case for you to purchase something.
If the device in question "doesn't make much of a case for itself", then it is failing to provide any compelling reasons for you to purchase and use it instead of one of the available alternatives; we can presume that its competitors are more capable, or cheaper, or easier to use, or better-looking, or some combination of those.
Edit to add:
In particular, the "for itself" is appropriate because a salesperson could "make a case for the phone" by explaining its benefits and features to you. In the absence of a salesperson, the phone has to have enough features and benefits that you can discover without assistance: the phone has to sell itself, or "make a case for itself".