Does the 'g' in fasmg mean generic?

yes

fasmg is a generic assembler that does not "by itself " know any instruction set but has a powerful macro language that can be used to implement instruction sets for any processor, some instruction sets can be seen here https://board.flatassembler.net/topic.php?t=19389 .

Thanks!

IIRC, Tomasz said it was just the letter following "f", as he was trying to implement the desired features for fasm2. As apt as generic seems the shadow of x86 and fasm are baked into fasmg - almost completely replaceable/extensible.

You probably have this post in mind: https://board.flatassembler.net/topic.php?p=174017#174017
But in the same thread I have also been mentioning "generic" as an explanation for the choice of the letter.

With ARM64 fast encroaching on the x86/64 world, this meaning (generic) is important, and reflects the purpose/milieu of the language.

Just to harp on the generic aspect, the bytecode block file assembler for my hobby VM is fasmg with some custom include files. Host applications can extend the assembler with definitions for their own custom opcodes by having their own include files as well. It ended up being a lot of bang for the buck.