Is this Landscaping Caulk on Outdoor Retaining wall Steps
Is this some kind of landscaping caulk?


No, that is an adhesive (glue) of an unknown type. It looks like regular construction adhesive to me.


  Would this product be an example of this...?


Yes


  should I... use it? Will it last for several years? ...would it be better to buy some kind of Mortar and use that to keep the stone steps in place? Do you think there's enough surface area to adhere to...?


I feel that the reason for the failure was poor original application. Also, since the original adhesive type is unknown, that also may have contributed if it was not a glue for exterior use.

Use the glue in your link but use way more of it than was used for the original bond, and try to scrape off all the old glue and clean all the mating surfaces first.