I think Gene's right. The original Kodachrome (introduced for movie cameras in 1935 and 35mm still cameras in 1936) had a film speed rating of 10. Kodachrome II, at "ASA" 25, didn't appear until 1961.
The "ASA 64" version originally was called Kodachrome X. I haven't been able to find a date of introduction for it.
Other potential color films in the '30s included various additive-process films (b&w emulsion with some form of RGB color filter.) Names back then included Autochrome, Dufaycolor, and Findlaycolor. These all produced a muted, pastel image somewhat like that of Polachrome film (a modern version of the same process.) The filter particles became visible if the film was enlarged too much, so these films were more commonly used in larger cameras, rather than 35mm. They were the standard for color photography for "National Geographic" for many years -- the magazine strongly resisted 35mm photos and Kodachrome. But the images on the Magnum page certainly look more like Kodachromes than additive-process shots.
So, most probably Capa made these on ASA10 original Kodachrome. The low speed rating may help explain why they're not as dramatic as his better-known b&w shots: with the old Kodachrome, you were pretty much limited to brightly-lit subjects that weren't moving too fast.