What font is used for the text in these games, or close? I'm not looking for Continuum, I'm well aware of its existence and it isn't what I'm looking for.

New Rodin  Suggérée par MatMayuga 
ShinGoPro  Suggérée par Circleheads 
Eurostile Bold  Suggérée par TristanBomb 

After I looked at it, it seems like Square 721, although it doesn't work on my computer very well and it isn't as close as I would like.

Agreed. Square 721 and Eurostile are very similar, but that "g"... Could be from other font (i.e. customized font for that game, but still based in major part on one of those fonts)

Yep, it looks a lot like Eurostile Bold with custom G and g. Thank you so much!
EDIT: Because SashiX didn't tag it, I will :P

Note that Eurostile has single small G and downwards-pointing small R. The font we're investigating in has double-storey small G and straight-pointing small R. So I don't think it's Eurostile, nor I do with Square 721...!

The font is called "New Rodin", by Fontworks Japan. http://fontworks.co.jp/font/classic/newrodin/L.html