Yes, many professional sequencing and playback systems can easily handle playing multiple videos with alpha-blending, there are numerous options, but I don't know of any that are free. There probably are some players that will handle it for free, but I've used commercial software and never had to dig in to it. (Update: There are free options, CasperCG was one quick option I found, but it looks like it has a rather involved list of requirements and setup.) To help with the keywords, searching something like "layering video player with alpha support" should give you a pretty good set of results with current products.
I recommend using alpha channel blending. While there are some real time chroma and luma key systems that run in software, the quality tends to be quite inferior to alpha blending or post produced keying.
Alternately, you can use two normal playbacks and a video mixer, though video mixers tend to be EXPENSIVE ($1000 for the cheapest HD one I know and $5000+ on average). They tend to have the best quality and most capability though and can also work reliably over live video.