No. Arbejde is work as in job/labour, virke means to work/to function (e.g "it's working" - "det virker"). Virke can also mean "seem" as in "det virker underligt" = "it seems strange/weird"
My answer for this task was "They are working for him" and I was told by Duo, that I used the wrong word. Why is the construction with 'to be' + -ing not accepted? Shouldn't it be supposed to be accepted as a correct answer?