Yes it will work as it does have "multi channel inputs" to hook up your DVD player. For $50.00 you aren't out much should you not like it and can always sell down the road.
Today's technology is much cheaper than years past. What you really should be considering are components with HDMI inputs / outputs. There are tons of used Blu-Ray players on Craigslist, Ebay, etc.. that can be had for $50.00 give or take. These will play DVD's as well as Blu-Ray discs. If you go this route, it's just one HDMI cable instead of 6 RCA cables you'd have to connect.
Are the speakers wireless or just the subwoofer? Hard to tell from the spec sheet.