When a Bomb token's Deathknell trigger is removed from the chain due to having no legal target for its "deal 2 to an enemy unit here" instruction, does the untargeted instruction to "kill all other Bombs you control here" also fail to resolve?

Yes — if there's no enemy unit at that Bomb's location when its Deathknell is finalized, the trigger is pulled off the chain at finalization (Rule 403.4) and never becomes a chain item at all, so "kill your other Bombs here" never happens either. "Deal 2 to an enemy there" is a mandatory choice with no "may," so with no legal option there aren't enough legal choices to finalize the ability, and the entire thing — both halves — does nothing.

Worth separating that from the case where a legal target exists at finalization but leaves before resolution: then the trigger does resolve, the 2 damage mistargets and does nothing, but the kill still happens, since "kill your other Bombs here" isn't a choice and doesn't reference the damaged unit.

So the Bomb's controller only detonates the chain reaction if at least one enemy unit was at that location when the trigger was finalized.