Why didn't Gazelle die when Merlin detonates the security chips?

The woman at Valentine's press conference (where they notice that she has an implant) is actually not Gazelle but some other assistent of him, who I'd wager wasn't as close/important as Gazelle to warrant an exception from the implant. As you can see, she has a significantly different face and haircut (which Gazelle never changes throughout the movie):

In fact, we see her again at other points throughout the movie. For example, when Harry sees her carry the invitation for the church event while visiting Valentine at home (where he also sees Gazelle, so they can't be one and the same person). Another point is when Eggsy is greeted by her when arriving at Valentine's base and hands her his weapons.

When looking at IMDb's credits I'd conclude that it is Johanna Taylor credited as "Valentine's Assistent 1" rather than Sofia Boutella's Gazelle.

The assistant in question isn't Gazelle, she is in fact another assistant also featured in the scene where Galahad/Harry walks into Valatine's home and sees the women with the leaflet for the church.

After the head exploding scene Valentine stated that he's not that stupid to implant an explosive version of the implant into himself. They both still needed the implant to be immune to the effects of the signal.

We can assume he did the same thing for his right-hand assistant Gazelle.

That woman in the expo wasn't Gazelle i dont think, just another politician