No; your stepson likely left after you told him to (he actually didn't have to follow this demand from you as it had no legal backing but he likely didn't know this). However, this doesn't mean you get to hold his possessions hostage until you get rent from him.
The advantage of going through the formal eviction process is that once this is received, you can dispose of his property (in the presence of a deputy/marshall) without your stepson coming back and suing YOU because you refuse to give him these items. And there are cases of tenants who have done exactly that when they've returned for items they've left behind and the landlord refused to provide them these.
In my county once the property touches the curb (hauled out by the "landlord" as the deputy/marshall does not help with the actual hauling, only oversees the process) the eviction is "over". You can then (if you wish) donate the property, toss it, have another family member haul it away to sell it, etc..
The only way legally to get owed rent from him is, sadly, to file a lawsuit against him in Small Claims Court. And even winning a judgement will not guarantee he will pay. For that you may need to consider garnishing wages or bank accounts. A sad thing to do to a step child.
Many people do not realize that a tenant is still considered a tenant even in the absence of a written lease. They are month to month tenants or tenants at will and can be notified they must leave with (in most states, although my state of Georgia requires a 60 day notice by the landlord) a 30 day notice from the landlord.
Gail