Your UPDATE transaction lasts just a few microseconds, so you can just centralise the problem and that's good because it's simpler, faster and safer.
But this is not a _distributed_ problem, as the article explains:
> remember that a lock in a distributed system is not like a mutex in a multi-threaded application. It’s a more complicated beast, due to the problem that different nodes and the network can all fail independently in various ways
You need distributed locking if the transactions can take seconds or hours, and the machines involved can fail while they hold the lock.