I'm still trying to figure out what that video is of. Is that a released Navy video or someone in Combat w/ a camera who thought Youtube would be cool?
The actual FLIR video (and not the video that's on Youtube) has been sanitized (the LAT/LONG and range has been fuzzed out), so I'm guessing this was either a briefing or something they're replaying to send back to Big Navy.
Regardless, it's not a real-time HAWKLINK video (ie the live feed) because, again, the data has been sanitized on the screen and not on the video from the camera.
Remember the 60B uses 1986's best technology. The video is originally on VHS tape. I am betting the ship has no way to digitize straight from the tape. I would guess that they are using the wardroom VCR to review the tape because. Filming the TV is probably the only way they have to get the video off ship rapidly.