The “g” is “god particle” should be lower case since it does not refer to any sort of diety. They are using the work to mean a basic sub-atomic particle from which all others are constructed. It is a bit chutzpahdik to call it such, but it does NOT refer in any way to “G-d”.
A “basic particle” is similar to saying that the basic element of Hebrew (and any other) writing system is a “dot” — put enough dots together and you can create any letter. No big hiddush.
Such research has led to many useful inventions in the past (radio, electronics, and nuclear energy being the most important commercially), which is why governments and private companies fund it. Whether basic scientific research is cost effective is a different matter, but certainly it is not ridculous to believe that it may, or may not, be worth the money.