Is H264 an actual file format?
I'd bet cash money they don't know what they're talking about when they say h264 format. There is a raw h.264 bitstream format, with the file suffix .264, but it's pretty obscure (I can't duckduckgo any actual documentation on what it's for, possibly when dealing with live streams from cameras). 

Give them an mp4 encoded with h.264 codec - it's a format you can be pretty certain anyone with software that's not completely obsolete can play. Conversely a .264 stream is fairly well guaranteed to be unplayable in all but rather specialist settings.

But if you have any doubts you could ask them if h.264 encoded mp4 is what they mean.