Old versions of Alien League have an incorrect internal name. There are several name fields that need to be filled in by the font's creator. Among them are the PS Font Name, Full Name, Menu Name and FOND Name. In the case mentioned here, three of the fields have the same name as what the font is supposed to be, but has Arial in the Full Name. So it conflicts with the real Arial font.
Google makes heavy use of Arial in the text it returns for a search. When you display such a page, the version of Alien League you had gets in the way of the regular Arial (Roman) font. Arial Bold will still be correct since that's a different internal name and a separate font, but all regular Arial text will display in the Alien League font.
Alien League has been updated and can be downloaded from most sites as a correctly functioning font. There are still bad copies out there, but they are actually getting very difficult to find. You can't go by the name of the font since both a bad copy and a fixed version are named alien5.ttf. Without a font editor to view the internal names with, you can't really know which is which without activating it and seeing if Arial suddenly gets trumped by Alien League.
So, long story short, if you really like this font, try downloading it from a few sites until you find one that works correctly.