And you know what? They're BOTH right!
Pits & Perils likes simplicity (quite a bit, actually) and so, ostensibly, race is class in the traditional way. But there's a lot more going on than just that, and the game acknowledges the flexibility that all races, and not just humans, would reasonably possess while holding on to that old-school spirit.
So, going class by class:
Dwarves and elves have clerics that only interact with their own kind; which is convenient, but consider that non-humans also have smaller, more homogeneous societies with no competition among their deities for worshipers. This stands in stark contrast to humanity, with their many gods all jockeying for supremacy, and this lack of evangelical zeal makes a difference.
But non-humans CAN be clerics.
Dwarves and elves are all de facto fighters, wearing armor and fighting with any weapon, and while they lack the +1 bonus of their human counterparts, their choice of weaponry alone makes a huge difference. There's really nothing more to say. Whatever else a character might be, they're also fighters...
|This dwarf has a lot more going than meets the|
eye, perhaps being a stay-at-home priest of even a cunning thief!
MAGICIANS: For elves, at least...
Dwarves are simply incapable of using magic, so this is largely excusable. Elves, on the other hand, are naturally magical and work as magicians in addition to fighting abilities, so they CAN be spell-casters, albeit with limitations.
THIEVES: For the agile, yes!
Lastly, dwarves and elves with the dexterity ability can forego armor and operate as thieves for all intents and purposes, climbing walls, hiding, sneaking, and stealing small objects. They can't disarm traps and/or pick locks, but this can be easily justified by the fact that non-human societies are different, and criminal behaviors less common. Of course, the referee could easily house rule the latter, perhaps at some sort of penalty.
But stealing things? That's thievery...
In defense of class restrictions, non-humans are mentally and physically different. For instance, the dwarven inability to work magic of any kind can be very easily defended on racial grounds alone, because their brains operate differently. Remember, these races enjoy many special abilities. And so do humans, although mainly in the form of greater flexibility...
Old-school simplicity is charming, and easier to work with, especially at the time of character creation. Pits & perils tries to have it both ways, and this may apply to other games if the referee (DM/GM) is willing to view class as a collection of abilities that often overlap, especially if they're OK with granting stealth to non-thieves when dexterity so permits.
Class as race? Sort of. But it's so much more than that!