TPE, thermoplastic elastomers. There are some different formulations, with the softer types tending to break down more. In some cases like buttons/keypads, they may be silicone rubber.
You can usually clean the goop off the surface with abrasion and strong, hot, detergent solution, but it is still breaking down, and if there are key markings (alphanumeric) printed on the surface, those may abrade away so sometimes less cleaning is better than trying to get a like new, clean surface.
Fortunately the TPE is usually an overmolding rather than structural member of the device so once you clean it, the device is still usable.
Just wait until society decides that everything plastic or rubber has to rapidly break down to be good for the environment, or that it is cellulose based instead towards same end. I don't mean to start an environmental argument as there are both sides to that, waste in mining/manufacturing and cost to build new, versus repair old in what is already a disposable product oriented society. It's just unfortunate for those of us who don't want to keep replacing products just to get the same job done rather than replacement being a worthwhile upgrade.