Powerwash, and keep the dirt and debris that it roots in blown away, or swept up.

Would a typical weed killer get rid of them?

It appears to be just moss and a completely natural occurrence in wet, partially shady or north or easterly facing aspects. Lawn weed killers will not address moss - purchase a lawn moss killer or carefully spray (away from the lawn) with a dilute bleach solution. You can also power wash instead but that will cause erosion of the concrete sidewalk eventually. FWIW, the moss will return after winter.

I have to do this several times a year on parts of my concrete walkway. Could also be caused by irrigation overspray.

I wouldn't be concerned about something that's not on my property, but if it bothers you that much, powerwash it and keep it clean as suggested. If your neighbors have moss too, then it will probably keep coming back.