That cable was all that was left of the original GM recall kit.
What you are talking about is a torque limiter. I do not recommend solid motor mounts for the street not because of the engine vibrations they transfer into the car (on a poorly balanced motor it will rattle your teeth), but because of the stress it places upon your aluminum transmission case. A better solution is a plastic motor AND a plastic transmission mount.
Whatever style of mount system you use, you must use the same type mount at all attachment points. If you go with solid Moroso motor mounts then buy the solid steel tranny mount (Moroso part number 62600); and be sure to use a lot of red Loctite because of the vibration. If you use a plastic interlocking motor mount use the transmission mount made of plastic as well or you will crack the case of the tranny with time.
As to chains and cables. There are two issues. First it can not be mounted to an aluminum head. A single bolt will transmit enough force to pull the aluminum head apart. If you have aluminum heads you will need a steel plate to attach it to the head (such as the A/C front mounting plate on the big block that bolts to the front of the head and part of the block to distribute the load). Second is where you attach the other end. It will be under stress and by definition it will be bending (stress is synonymous with deflection in engineering). So if you are attaching it to your front suspension expect your steering to change when the cable/chain pulls on it.
Race cars all use a front and mid mounting plate to attach the motor solidly to the frame. Your car doesn't have a frame (a sub frame yeas but that gets bolted to sheet metal unless you have sub frame connectors and a roll cage to make a frame). As such I do not recommend a mid mount front mount system for the street.