according to Wikipedia she also holds the more prestigious international master title
It's perhaps worth starting by identifying the difference between an IM and WGM title. According to the latest FIDE regulations - FIDE Title Regulations effective from 1 July 2017:
1.48 Performance Rating (Rp)
In order to achieve a norm, a player must perform at a level at least of that shown below:
Title - Minimum level prior to rounding - Minimum level after rounding
GM - 2599.5 - 2600
IM - 2449.5 - 2450
WGM - 2399.5 - 2400
WIM - 2249.5 - 2250
1.53 To have achieved at some time or other a rating as follows:
GM ≥ 2500
IM ≥ 2400
WGM ≥ 2300
WIM ≥ 2200
So, an IM title requires 3 norms of a 2450 performance plus a live rating at some time of 2400 while a WGM title requires 3 norms of a 2400 performance plus a live rating at some time of 2300. That means the rating difference between the two titles is just 50(norm)/100(rating) points. That isn't such a large gap.
Why do they not introduce her by also mentioning her higher achievements?
There is no rule requiring them to introduce her in any particular way. Generally speaking on these shows the presenters are introduced the way they want to be introduced provided it is truthful.
Famously, Judit Polgar refused to take any women's titles and only ever applied for open titles. That was her way of fighting for women's recognition in the chess world. I suspect that Houska is taking a different route by asking to be identified by her women's title. That is also a subtle way of making the point. She is a top class international player and a woman.