Thanks MDM, that chart gives me a very straightforward answer. No, he does not need to file a return. Interestingly for anyone else following along, Publication 929 (2017) goes into a little more detail with examples. Specifically, make sure to check out Chart C on the 1040 Instruction sheet below where MDM linked, as there are a few other situations where a dependent would have to file a return even if they didn't meet the various income thresholds detailed in Chart B. Also, as is pointed out in Publication 929, if the dependent had ANY federal tax withholding from earned income, they need to file in order to get their refund.
Publication 929 also detailed the situation in which you must include some of your child's unearned income on your own return, and that threshold starts at $2,100 of unearned income, so he/we are far away from that.
However, all of these rules refer to dependents on whom you claim an exemption. I wonder how the rules will change with the tax codes changes removing exemptions, since on the 1040 form it is under the exemption section where you officially list your dependents, their SSNs, and relationship.