Don't waste your money. I bought the Remington 870 shotgun collapsible buttstock kit (AR-15 style with pistol grip and 6 position collapsible buttstock). Looks like the buttstock you reference. It is pretty cheap, and would be a lateral move at best and realistically probably a downgrade compared to the 15-22 standard buttstock.
I bought a Magpul STR for my 15-22 and like it a lot. I have a CTR on my AR-15. Hard to beat Magpul's products. I also am quite impressed with their customer service.
I recently participated in their "Operation Boulder Airlift" to supply Colorado residents with much needed supplies of PMAGs. (There play on the "Berlin Airlift" of WWII). Got mine recently after just a couple weeks wait. Sorry, a bit off topic, but just cannot say enough about the company and its support of customers in Colorado.