Employees are only required to work in the sense that refusal to report can result in discipline (like reprimand or firing) and forfeit of whatever money you would have earned had you shown up. This is exactly the same way federal employees (or most employees, for that matter) are always required to work. The fact that they're not being paid on time has nothing to do with whether it's slavery. That's because pay has nothing to do with slavery. Slavery is forced labor and/or ownership of people, and civilian federal employees are just as free to quit as they normally are. Military personnel can't freely quit, but they can never freely quit. Nothing relevant has changed for either group.
Not paying employees is potentially a violation of labor law, and the government in fact lost a lawsuit after the last shutdown for violating the FLSA. If that happens this time too, they'll have to pay damages.