Melted Exterior of the Alienware M14x-R2?

This is not your fault - Dell has known issues getting this right on the 2nd gen laptops, all the way up until Ivy Bridge. Even some of the Haswell/Broadwell machines had problems. It’s one of the reasons I began to like the aluminum HP Commercial products once they removed the WLAN WL, and why I put up with some of Dell's poor QC on the machines up until Haswell, outside of pre Haswell HP. Anything newer can go either way as Dell has had fewer issues with it now, but generally HP>Dell.

This is generally just a coating that went bad, with actual plastic underneath. What you need is to get denatured alcohol to clean it (either take the laptop apart or cover EVERYTHING you do not want this to touch - it’s not fun to clean when it spreads in large chunks - taking it apart is best). You'll need a throwaway cloth as there's just no good way to wash it afterwards. Test a small area first and see, and if it comes up then you can salvage it. You may need a new palmrest if it doesn't come up cleanly.