I think we are in agreement here, peak X (crude, gold, dodo birds) production means the highest number of units produced what will not be surpassed, ever. In the case of crude oil it happened in 2008, I have tried to find a chart, but they keep mixing in all kind of oil, so it is not so obvious for the Average Joe.
And you are also right that even replenishable products like the dodo bird, or timber can reach a peak production number as long as the rate of replacement is slower than the rate of usage. When they discovered oil in Pennsylvania that was the time when whales were peaking and they almost went extinct because of over whaling...
One more note, different geographical areas have different peaks. Crude oil peaked in the USA back in the 70s, even coal peaked in the 90s, in absolute numbers. (that is a whole new bag of worms)
So I think we generally agree, every non-replenishable product's production peaks sooner or later.