There is a note on page 23 of the HyperDeck manual which says:
Currently, HyperDeck Studio Mini will play back H.264 files recorded on a HyperDeck Studio Mini, but not H.264 files recorded on other video equipment.
So it's not a huge shock that this doesn't work. With H.264 files there is a wide range of possible codec variations, and probably not all of these codec options are supported by H.264 decoding support on the HyperDeck Mini. With ProRes this is less of an issue as the codec is much more tightly constrained to a few possible encoding options.
Presumably if you exactly match the codec settings (including resolution, frame rate, bitrate, profile level, entropy encoding, B-frame usage, audio codec, etc.) of a file recorded on the HyperDeck Mini, you'd have a chance of playing it out. Maybe.
Given all of this I have a feeling that ProRes may be a better option for external files you intend to use for playout on the HyperDeck Mini.