Shouldn't this compound be called 2-methyl-5-(1,2-dimethylpropyl)nonane?
‘5-(1,2-Dimethylpropyl)-2-methylnonane’ is not the preferred IUPAC name. The preferred name according to current IUPAC recommendations is 2-methyl-5-(3-methylbutan-2-yl)nonane.
If this is a homework exercise, however, it might be based on obsolete IUPAC recommendations from 1979 or 1993.
You are partly correct; simple prefixes are arranged alphabetically disregarding any multiplicative prefixes. The multiplicative prefixes are inserted later and do not alter the alphabetical order. For example, ‘1,2-dibromo-’ is considered to begin with ‘b’.
However, the name of a compound substituent is considered to begin with the first letter of its complete name. For example, ‘1,2-dibromobutyl-’ is considered to begin with ‘d’.
Likewise, ‘1,2-dimethylpropyl-’ is considered to begin with ‘d’. Therefore, it is arranged before ‘methyl’.