I don't know what the reason is on the Ffestiniog, but I think I've seen published photos from many decades ago showing right-hand running. I wonder whether it dates right back to the 1830s and if at that time there wasn't yet an established national convention about which track trains used. That's just speculation, though.
First, let’s get over the convention issue, the FR (being the oldest independent railway in the world) follows its own conventions, and where required in terms of safety follows Government (e.g. today the ORR) guidelines. Looking at individual stations:
Minffordd - essentially the up line was for passenger services and the down for mineral (gravity) trains destined for the yard. This existed until about the 1920’s when passenger trains crossed here and there was no logical reason for changing to LH running
Rhiw Goch - can work LH or RH, but for convenience is generally LH so up trains have a straight run through against the grade, but changes to RH for gravity trains to save having to slow down to negotiate the loop.
Tan-y-Bwlch - again historical based on the shunting of goods waggons destined for the goods shed before vacuum brakes were fitted in Victorian times, etc. etc.
Tanygrisiau - was for a while LH running, but now RH as much easier due to the curve for the guard to see the driver.
All very logical.