The solution you propose would work fine. Keep in mind that you'll need to run 2x Cat6 to each display to use that matrix. A couple points though:
First, seeing as you are only using one source, why not go with an HDBaseT solution
for the same cost as the matrix? This only needs 1 Cat6 run and is a much more robust solution. In the future if you decide to add more sources, you can always add a cheap HDMI switch or an A/V receiver.
That brings me to my second point - if you're running new Cat6, seriously consider running speaker wire as well and putting at least 2 decent speakers in the 2 locations (especially outside). This will greatly improve the audio and doesn't all have to be done at once if budget is a big issue. For example you could:
- Run the Cat6 and speaker wire now and use the splitter I recommend above
- Later add the speakers and an A/V receiver with 2 zone output
Edit: also, run more Cat6 than you think you'd need. Its so versatile if you decide to change things in the future.