This feels more like some company has some device or program running from all over the place, and for whatever reason got their DNS pointed at you. A botnet is

This feels more like some company has some device or program running from all over the place, and for whatever reason got their DNS pointed at you. A botnet is generally used in an attack, not just creating random spam. Personally, I wouldn't worry about it. If you're really curious, I'd do two things: First look at where the IPs geolocate to. Do most of them come from a particular country or region? A particular ISP/AS? Maybe a particular type of ISP (eg mobile carrier)? Further, you might look at when these requests are made, how frequently they recur from the same IP, etc. Second, do a packet capture and look at the full request. Maybe it'll have a hostname or telltale header, etc.