Those replays are probably from a different version of demigod. Like 1.2 patch, 1.0 or something. And the sad part is that old replays cannot be seen on the newest 1.3 version...
But there is quite a decent amount of 1.3 version replays also, which can be seen with this version, or just save the replays of your games to watch them. (hint to tournament matches of great players, which were saved and got links to them http://forums.demigodthegame.com/399047)
P.S. I've got huge amount of replays from many matches, So if you need anything, I can share with you (includes all range of players/demigods). Saved ~90% of my played online matches, except very short ones, crashed ones, etc.