Why is this not "Acque Terme"?
According to the website of the town http://comune.acquiterme.al.it/la-citta/noticia/la-storia-del-comune-di-acqui-terme, it was founded by Romans on the II century B.C. and the latin name was Aquae Statiellae.
From late antiquity it appears as Acquis that in vernacular will become then Acqui. This means that Acqui is not a different gender but a different latin case.
The second term "Terme" was added officially in 1956.
You got an excellent answer already, but I would like to point out more explicitly that in Acqui Terme the word Terme is not something that needs to agree with the name of the town, but rather a modifier that indicates the presence of thermal baths near the city.
This is in fact a relatively common phenomenon. Let me show you some examples
In the first two cases, this is also to advertise that the town is in a different location than the "main" town of the same name, and specifically on the beach front (Lido meaning coast and Mare meaning Sea). In the nearby coast you can see several more examples of this.