Technically speaking from a historical standpoint, the personification of death has always been a skeleton, which is true, for the most part. But the reaper garb, no. That was created during 14th century Europe when the Black Death was roaming around.

If you look at other historical cultures on their representation of Death, you'll find a lot are actually cloakless and scythless. Look at Mictēcacihuātl, she was the Aztec Deity of death and sported no cloak, no scythe, nothing. Same with Yama, except the only difference is that he actually had flesh. Blue even!

I always forget about Chronos. Didn't really stick with Roman Mythology. But he is too a deity of death. He does sport the scythe but no cloak and no skeleton.

So I guess sorry that a Japanese game didn't choose the one representation of Death that you wanted.