Schengen has independent of the EU status. Eg. you can move freely from Germany to Switzerland (without obligatory border check) but not between Germany and EU-member Cyprus (there is the obligatory border check).
Schengen governs border controls, not the right to work and residency, which is a function of EU membership, not Schengen membership.
I think Switzerland has a bilateral agreement with the EU (or via EFTA) that allows for free movement and employment of people, so they enjoy these freedom as well despite neither being in the EU nor the EEA (but they are a member of EFTA).