The problem is in TABLES.INC (EIP/RIP is added as an addressing register but not in the reserved symbols table).

BTW, why the tables are hand-made instead of defined more safely with the interpreter layer and maybe with the preprocessor as well?

You're right, the addressing registers table is not scanned when checking for reserved words - perhaps the simplest fix is to include EIP/RIP in main symbols table, too

The EAX points exactly where it should.

And as for the hand-made tables - that's mainly because I try to keep fasm's sources assemblable even with very basic version of compatible assembler - without any macros or advanced features.
It is for two reasons: one is, that is it a relict of the early times, when fasm was written and assembled with my very simple previous assembler (and it just stayed this way); the second reason is that I considered to write a very simple "startup assembler" in C, that would be used to make fasm from sources on linux systems starting with only C compiler. I never did this, but I still think that would be a good idea - maybe someone else would like to do it?

haha, well RAX actually and yes I did know that, what I tried to point out was that "[rip]" used the RIP register instead of the rip label (that shouldn't be allowed to be defined like eax label).

Interesting idea that "startup assembler", candidate to be included in Project and Ideas forum. Could you create a thread and post the minimal feature set required for assembling fasm sources?