Does the Droid Turbo only support one kind of font? and if it supports more than one, which Construct 2 fonts will mobile phones support? It's really disappointing that the Droid Turbo, if that is the case, does not support a variety of fonts. Construct 2 offers a variety of fonts that can be used in projects.
To be clear, Construct 2 does not offer any fonts. The fonts available to you in Construct 2 are those it has found installed on your computer. Different operating systems (Windows, Mac, iOS, Android etc.) offer different fonts. Even two Windows 7 PCs will not have all the same fonts, although they all start off with the same basic font set, but not the same basic ones as on a Mac or a Windows 10 PC.
When you use a font, for example, Tekton Pro, in a game that is then displayed on my PC, my PC goes to look up if it has that font installed. If it doesn't, it looks at a font substitution file that says "if Tekton Pro isn't found, use an alternative that is in the same family of fonts" (decorative, serif, extra bold, whatever). What your phone is doing, because it doesn't use Windows fonts, is substituting your Arial with its own installed font substitute (which may look identical to Windows' Arial but will probably be something different). Your phone is telling you that all of the different fonts you have tried in the game you have designed are in the same font family as its built-in "Arial substitute" and so it uses that.
The above is, in general, why you shouldn't ever use anything other than web safe fonts in HTML5 games and if you're going to upload them to iOS or Android you should stick to the very plainest Arial-type fonts (which can still prove hazardous depending on the character set you use) or, as already advised, use Sprite fonts which have a bigger payload but over which you have complete control.