Honestly... I think it's really, really stupid.
First, the Techichi hasn't been around for a long time. They were also supposedly long coated and mute... the "current Techichi" breeders are breeding for ~10lb, short coated, fawn colored dogs... and I'm sure they're not mute
Breed standard says the chihuahua is supposed to have an apple domed head. This is, in fact, a dominant feature. Two apple headed chihuahuas rarely have a "deer" headed offspring.
Chihuahua breeders who breed for the "deer" shaped head are BYBs. This would be like, say, breeding for GSDs with floppy ears.
It's honestly easier and cheaper to produce deer headed chihuahuas. They tend to be larger (females can hold more puppies and birth them easier due to head shape), they're available without neuter contracts (since BYBs are breeding them and don't care if they're sold and then bred), etc.
Calling a chihuahua that is out of breed standard a Techichi just makes no sense, considering Techichis have been gone for so long. It's just an excuse for BYBs to produce their poorly bred dogs while calling them something new and exciting.
Anyway, if you've seen any of the ancient artwork/statues/toys of Techichis, a lot of them look like apple heads:
If people really want to make the split and are health testing the "deer" head chihuahuas and coming up with some type of standard, it would be one thing. Calling them an ancient type of dog just makes me shake my head.