It seems you are right FeiLing. The War Chariots, Camel archers and Keshiks get bonus production from Temple of Artemis and NOT from the stables. They are it seems really classified as archery units and NOT mounted units. However, all descriptions in the civilopedia calls them ''mounted'. For example I wll quote the end of the civilopedia entry for:
Chariot archer: ''As a mounted unit, the chariot archer is vulnerable to spearman'';
Camel archer: ''As a mounted unit, the Camel archer is vulnerable to pikeman'';
War chariot: simillar entry;
Horse archer: simillar entry;
War elephant: simillar entry;
Keshik: has NO such entry: They are only referred as mounted warriors in the text, maybe a reference to real history and not the game mechanics.
Conclusions:
1. this is either a bug and these units shouldn't be classified as archery but mounted units ( I could swear they were in vanilla, but I am not really sure)
or
2. this is a correct classification and civilopedia needs to be corrected.
cheers!