In answer to your initial question, I would agree with Prof. Herbener in stressing that scarcity is a purely quantitative phenomenon, in the sense that a given stock of a particular means is scarce if the available amount of it is insufficient to satisfy all the wants that could be satisfied with it. So, if you have 1000 pails of water in your possession and can potentially utilize 2000 pails of water to satisfy various ends, then a particular quantity of water (say, 500 pails) is a scarce good because the satisfaction of certain ends are dependent on your having the water in your possession. In other words, if you lose the 500 pails you must endure some loss of satisfaction.
However,, if the available supply of the means is more than sufficient to satisfy all your ends (so if, for example, you have not 1000 but 2500 pails of water in your possession), then water is no longer scarce in that losing an amount of water that is less than 500 pails does not involve any loss of satisfaction. For a detailed analysis of the nature of scarcity along these lines see Menger’s Principles (Chapters 2 and 3) and Bohm Bawerk’s Positive Theory of Capital (Book 3, Chapters 1-3).
Regarding your follow up question, I would argue that what Mises is trying to say is that we do not make any choices with respect to a good that is not scarce. Thus, we do not allocate units of goods that are useful but available in abundance (in the sense outlined above) amongst ends or purposes. We do not, for instance, allocate a breath of air to the purpose of breathing and not to some other use, since we do not give up any other ends in using that amount of air to satisfy the end of acquiring oxygen. The stock of air available is so abundant that we can waste a breath or in fact a roomful of air and not face any potential loss of satisfaction because this does not impair our ability to satisfy wants in the least.
Similarly, in your example you are not engaging in choice with respect to those boards. You are not allocating them to one purpose or end (exercising) in preference to other ends that could also be satisfied using them (if the boards were not as durable as posited in your example you would still be engaging in inter-temporal choice with respect to them, i.e., using the boards now would entail not using them to satisfy the same end in the future). That is what Mises means when says that there is no action with respect to those elements of man’s environment that are not scarce.