A VCR with a composite out would work. But what do you mean by having a hard time to recognize the signal?
Are you sure the output isn't directly composite? Try stripping a rca (composite) cable and connecting it to your tv that way.
That looks to be pretty old but the output is in NTSC-J for sure.
NTSC-J and NTSC for the US/Canada is the same except that you have to put the brightness higher. It should sync right away on a NTSC TV. Also, if it doesn't work on channel 3, try channel 4(or 2 ) since Japanese VHF goes from 1-12 while US VHF goes from 2-13 and that game could be outputting to channel 3 in jap vhF.
And yes, that adaptor should do the trick, but it should still work in 300ohm...