There are probably even closer fonts out there, but I ran out of patience while hunting through FontSquirrel and Google Web Fonts. There's no good way to search for a font that "looks like Eurostile", since all the classification systems are too broad to be useful or too fine-grained for free font designers to bother with.
Since Dissidia 012 (and possibly some other games) uses the Japanese font, not the Latin one, something else to look at if possible would be using the Japanese characters from a free Japanese gothic font but replacing the Latin with the chosen Latin font. Some licenses allow this; others don't.
For reference, here's a small New Rodin specimen: http://fontworks.co.jp/font/sample/data/newrodin.pdf
The PSP font is the DB (demibold, 600).
Edit: After taking a look at this very small specimen of VL Gothic and Sazanami Gothic, I think Sazanami Gothic is a little bit closer to New Rodin's kana but VL Gothic's heavier kanji are more similar to New Rodin DB's kanji. There are few free fonts with kanji, but a lot more with just kana, so an optimal solution would call for splicing three different fonts together. That sounds absurd to someone in the Latin tradition, but it's not uncommon in Japanese typography.
Since Dissidia 012 (and possibly some other games) uses the Japanese font, not the Latin one, something else to look at if possible would be using the Japanese characters from a free Japanese gothic font but replacing the Latin with the chosen Latin font. Some licenses allow this; others don't.
For reference, here's a small New Rodin specimen: http://fontworks.co.jp/font/sample/data/newrodin.pdf
The PSP font is the DB (demibold, 600).
Edit: After taking a look at this very small specimen of VL Gothic and Sazanami Gothic, I think Sazanami Gothic is a little bit closer to New Rodin's kana but VL Gothic's heavier kanji are more similar to New Rodin DB's kanji. There are few free fonts with kanji, but a lot more with just kana, so an optimal solution would call for splicing three different fonts together. That sounds absurd to someone in the Latin tradition, but it's not uncommon in Japanese typography.