You are correct in assuming that this is a moire issue, rather than a 50/60hz banding issue, which can be solved as suggested above.
Moire however, is caused by line skipping on the sensor. The only way to completely eradicate moire in this situation is to use a camera that uses every single pixel to capture video. This basically means using a dedicated digital cinema/video camera which natively captures every pixel or a DSLR or M4/3 camera in crop mode (Available on GH4/GH5 or on Canon DSLRs using magic lantern, not sure about others.)
The simpler way to solve the issue is to shoot the computer screen ever so slightly soft so the banding isn't visible and then apply some sharpening in post to recover the edges. Not perfect, but a reasonable compromise.