Spiritual means honouring sacredness (
see here).
The concept of sacredness comes from religious beliefs. These beliefs need not be ingrained in the religion (like christianity and alcohol).
This is what i think it means:
A religious muslim prays five times a day, doesnt eat pork, etc.
A spiritual but not religious muslim wouldn't eat pork, but doesnt pray five times a day.
Atheists have no such qualms about spirituality. They may follow a lifestyle percieved as spiritual, but the reasons behind them are certainly not.
I hope this helps.