I played Brynhildr Thundersong, then killed my opponent's Machine Evangel. Does my opponent get Machine Evangel's deathknell or no?

Yes, your opponent still gets the Machine Evangel's Deathknell effect.

According to the established rulings for Brynhir Thundersong (specifically RiftJudge FAQ #8909 and #5853):

1. Brynhir's restriction is limited: Brynhir's "When you play me" effect only prevents players from playing cards (taking them from a zone and placing them on the chain).
2. Deathknell is not playing a card: A Deathknell effect is a triggered ability that resolves automatically when a unit dies. It is not considered "playing a card," so it is not restricted by Brynhir Thundersong.
3. Tokens: Furthermore, as confirmed in RiftJudge FAQ #6800, tokens are not considered cards, which is another reason Brynhir's restriction does not apply to this effect.

Therefore, when the Machine Evangel dies, its Deathknell will trigger and resolve normally, creating the three Recruit unit tokens for your opponent.