I haven't seen that engine model number. But the 170 part suggests about a 240cc displacement (70 is probably the bore size). Hawks, Storm, and others use a 169Fxx (69mm bore) engine, and 172Fxx engines (249cc) are in some other models.
The TDR you got seems to be closely related to the Hawk and Storm. Not sure why they named it a 300. Displacemnt is closer to 240cc.
BUT, that rear axel and swingarm design is VERY COMMON on these bikes. You should have no problem installing a universal rear axel tensioner. Here is a picture of a Hawk tensioner:
I don't know why you can't set the tension. You seem to have the parts there. Here is one from ebay. Google this description and it should find the listing:
"2X Rear Wheel Chain Adjuster Set Replacement For Hawk 250 Carb and DLX Models"
This one is from China ($16.99) plus ~$6 shipping, so it will take a week or two to get here. I saw a used rear axel tensioner on ebay for $20 (one side). But you probably have tall of tghese parts. It just needs to be set up and tensioned properly.
