The handles are made using a process called injection molding. They are likely nylon.
As for the rest of the information you are interested in, I doubt you will ever know.
It looks like they were just another import company importing products from China, and went out of business. Not an uncommon story.
It also looks like they pre-date the internet, which can explain the lack of information about the company. I found trademark applications for two different references for "Sportsman's Dream", one from the late 1970's through early 1980's, and one from the late 1990's to the early 2000's, both applicants selling cutlery, but I don't know which one, if either one, sold your knife. There is no other information included in the trademark records to provide any further leads of investigation.
I read that paper insert, and it says to wait 6 to 8 weeks for a refund or delivery of a replacement knife. Waiting "6 to 8 weeks for delivery" is definitely an old, pre-internet concept.
The set I posted before doesn't have your particular knife in it, perhaps there were different sets, or maybe the owner of that set lost or ruined that knife. I saw this set that does have the same knife (red arrow), described as a "bait and paring" knife on the paper insert. This set was also sold under the name "Sportsman's Dream".
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