Yes, you have it right. You will need 2 S-Video cables, and 4 RCA/composite cables (Red/White audio).
JVS Player
OUT
S-Video
RCA Left/Mono Audio (white) connector
RCA Right Audio (red) connector
ES10 (assuming using line 1 input on rear, select INPUT on your remote and change to Input 1 (INI1))
INPUT 1 (connect cables from your JVS)
S-Video
RCA Left/Mono Audio (white) connector
RCA Right Audio (red) connector
OUTPUT (to your capture device - assuming it has S-Video Inputs)
S-Video
RCA Left/Mono Audio (white) connector
RCA Right Audio (red) connector
If your capture card has only component inputs (red/blue/green) you could connect your ES10 to your capture card using those instead of s-video.
You might also want to look over the recommended ES10 settings posted on this thread:
https://forum.videohelp.com/threads/...15-DMR-ES25%29
Any questions/problems just ask! Cheers.