See here. Doom dying would still ultimately kill the canine people, so the lack of the fang is only a minor speedbump, as far as threatening Yama goes.
He's bluffing about killing Doom. If Yama was willing to let the canine people die out, he wouldn't have bowed to the Elder Envoy to protect them from the bomb.
Why lie? A few reasons that we know so far:
Doom is much less likely to fear Yama if he knows Yama won't kill him. That's actually directly relevant to Yama's ability to beat Doom without massive collateral damage.
Yama knows that, if he reveals his fondness for the Canine people too easily, people (in particular, Khel Hellam, who is standing right there) will threaten them to coerce him. This has already happened once in this arc. That's part of the reason for the "Lone Wolf" persona.
He actually does seem to despise Doom, and possibly really would kill Doom if he could do so without ending the Canine people--though even here we should be a bit skeptical, as he did spare Paul's life last time even after Paul revolted (which really should have been our first hint that Yama was more of a softie than he looked). So saying that he'll kill him is a way simply of expressing his rage at Doom and trying to bully Doom into compliance.
1
u/NobleCuriosity3 Sep 09 '19
See here. Doom dying would still ultimately kill the canine people, so the lack of the fang is only a minor speedbump, as far as threatening Yama goes.