I always read ‘eaten’ as ‘assimilated’ whenever the Tsaesci are discussed. To illustrate the point about Mysterious Akavir: the very next sentence after saying that the Tsaesci tried to eat all of the dragons it says that “they managed to enslave the Red Dragons, but the black ones had fled to Po Tun.” I also remember reading somewhere that they used those Red Dragons as war mounts, which I think makes far more sense than simply eating them.
That's one interpretation, and since a lot of the Imperial Legion and Fighters Guild techniques were passed down from the Tsaeci, and the Battlemages sometimes use drakes as war mounts.
BUT...there's the http://www.imperial-library.info/obscure_text/tsaesci.shtml. Apparently they are QUITE fond of eating things which give them power.
This part of the lore may be rooted in certain real world superstitions from all over the world - ancient rites which sometimes included cannibalism, where tribal warriors believed that eating the remains of a fallen foe, either beast or human, transferred the powers or even the soul of that foe into the warrior. This mythos is even hinted at during a scene in the anime classic Princess Mononoke, wherein a tribe of sentient apes wishes to consume the flesh of a man to consume the power of man and fight deforestation.