My concern at this point is that there should be sofware on this machine to interface with the other?
LapLink
You have DOS 3.1 running on the IBM 5150, and thus you should be in a position to run the MODE command of DOS on the 5150. If you do, then what you should be able to do with your serial LapLink cable, is run a DOS version of LapLink on your GateWay (after booting to DOS), and then use a feature in LapLink that pushes LapLink down the serial LapLink cable to your 5150.
You can see that process being utilised within the procedure [
here], although note that that procedure is for a different situation (use of a 'modern PC').
By the way. That 'push-down-the-wire' feature will not work using a parallel LapLink cable. It has to be a serial LapLink cable.
Once LapLink is running at both ends, do the file transfers via LapLink. For faster transfers, upgrade from a serial LapLink cable to the parallel version (changing the configuration of Laplink at both ends accordingly).
A potential LapLink problem
If there is a significant difference between the 'speed' of each machine, then timeout errors usually occur. For example, if I connect my 6 MHz 5170 up to my 486DX-66 clone, they won't communicate until I use the turbo button to drop the 486DX-66 down to 8 MHz. Others on these forums see similar. So, you will probably need to use the turbo button on your GateWay to drop the GateWay's speed. Maybe the drop in speed will not be enough.