Definitions of the alpha wave in the revised glossary by Clinical Neurophysiology Practice?
I personally don't see the contradiction. It seems very contrived from your end to establish that there is one. I think it's very clear from the definition of the alpha wave that 'duration' is synonymous with 'period' in that case. In the 4th quote, defining 'duration', it even says this outright, "The duration of the cycle of individual components of a sequence of regularly repeating waves or complexes is referred to as the period of the wave".

Basically, looking at the definition of alpha wave where duration in that specific case equals period, solves everything. It's the most intuitive answer. Would it have been better if they had written 'period' instead? Probably. But to pick up on that definitional ambiguity, not see their definition of duration also includes that of period, and somehow claim that this implies people are defining alpha waves for non-cyclic activity is an enormous stretch.

The glossary's definition is correct and you can understand the definition of an alpha wave as a wave in the 8-13 Hz band / a wave with a period of 1/8 - 1/13 seconds.