sending the same query at the same time
QUERIES DO NOT ALWAYS RUN IN PARALLEL
It depends on the database engine. With MyISAM, nearly every query acquires a table level lock meaning that the queries are run sequentially as a queue. With most of the other engines they may run in parallel.
echo_me says nothing happens at the exact same time and a CPU does not do everything at once
That's not exactly true. It's possible that a DBMS could run on a machine with more than one cpu, and with more than one network interface. It's very improbable that 2 queries could arrive at the same time - but not impossible, hence there is a mutex to ensure that the paring/execution transition only runs as a single thread (of execution - not necesarily the same light weight process).
There's 2 approaches to solving concurent DML - either to use transactions (where each user effectively gets a clone of the database) and when the queries have completed the DBMS tries to reconcile any changes - if the reconciliation fails, then the DBMS rolls back one of the queries and reports it as failed. The other approach is to use row-level locking - the DBMS identifies the rows which will be updated by a query and marks them as reserved for update (other users can read the original version of each row but any attempt to update the data will be blocked until the row is available again).
Your problem is that you have two mysql clients, each of which have retrieved the fact that there is one item of stock left. This is further complicated by the fact that (since you mention PHP) the stock levels may have been retrieved in a different DBMS session than the subsequent stock adjustment - you cannot have a transaction spanning more than HTTP request. Hence you need revalidate any fact maintained outside the DBMS within a single transaction.
Optimistic locking can create a pseudo - transaction control mechanism - you flag a record you are about to modify with a timestamp and the user identifier (with PHP the PHP session ID is a good choice) - if when you come to modify it, something else has changed it, then your code knows the data it retrieved previously is invalid. However this can lead to other complications.