it is possible for your machine as it is (compatable with the software you have already)
to run programs compiled with -march=pentium4
anything less (older) than that but for intel is ok as well.
http://gcc.gnu.org/onlinedocs/gcc-3....002d64-Options
just so you know how far back you are going when you use code optimized even for 686
as for what uname -i says mine says "unknown"
-i is short for hardware-platform which seems quite vague when you consider the wide range of platforms linux will run on and what would amount to thousands of names like "Sun Enterprise 3000" on and on
so i think the use of uname -i in the program or script you mention is a mistake and they should use
uname -m would work better. The whole thing is a mess and what it amounts to is your machine running code compiled for a processor 386 from 1985 -- lets see in one month that will be 20 years ago !