Iirc the PS2 also got a huge boost by being a cheap alternative to designated DVD players, but it eventually obviously paid off. I wonder how that factored into their PS3 strategy
Indeed, although Sony hadn't created the DVD format (Phillips), having it did boost sales of the PS2. With the PS3 Sony was pushing its own format in direct competition to HD-DVD (also Phillips), and I'm sure losing Beta max market to VHS was still in their minds. So they decided to sell PS3 consoles at a much greater loss. It did pay off as well, but the first few years cost Sony a lot.
I purchased my XBox One for the same reason (cost-effective Blu-Ray player with the possibility of playing games from time to time).