I briefly looked into this a while back
And the simple answer is Yes,
there will always be some sort of usage or licencing terms for fonts.
Many of the better font sites have an accompanying information or a text file explaining usage rights. But many dont.
rights can differ wildly for commercial use from (free with attribution) to (contact the rights holder for commercial use) to (licencing based on sales)
I think it is really up to the game developer to do a reasonable amount of investigation to establish rights for the fonts they are planning to use.
but it is a bit of a minefield out there.
there are many very small variations of fonts with very different usage rights
and I also believe there are many companies trying to make money claiming rights for font designs that they really didn't own.
so as I said a documented and reasonable amount of research into establishing rights even if you cant establish the rights.
just in case your game goes viral and the font designer / owner pops up with a claim. at least you have established intent. which is what the courts will be interested in.
I am not a lawyer this is just my view based on limited research.