Is it possible to add a spatial index to a partition with Postgres 10?
As documented in the manual


  Partitions may have their own indexes, constraints and default values, distinct from those of other partitions. Indexes must be created separately for each partition 


(emphasis mine)

So as you are using Postgres 10, you need to create that index manually on each partition (the part you quoted from the manual even shows that the indexes are created for each partition, not for the partitioned table).



With Postgres 11, indexes can defined on the master table and will automatically be created on each partition. 

If you need partitioning you should consider upgrading to Postgres 11 anyway as that massively improved the partitioning capabilities (including performance)