The reason this does not qualify as double spend is because only one of these transactions (the one recorded in the longest history of the Bitcoin blockchain) is considered a valid network, while Bitcoin in another transaction cannot be spent because the network that does not valid.
The reorganization meant that an 'obsolete block' (also called an 'orphan block') was mined containing bitcoins that were also issued to the active bitcoin chain, so a transaction with the same bitcoin was recorded on both the relevant and the irrelevant chains.
In this scenario, "it is important to know that yes, there may be different versions of the same transaction, but ultimately only [one] will be accepted by the nodes and users of the Bitcoin network" - posted by Lucas Nuzzi, Coin Metrics, Bitcoin Network Data Analyst on Twitter.
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