Does that RTC support a backup battery and alarm/wake up signal? Not all of them do. I don't see a battery in that image.
There's a coin cell included, a separate power supply for the RTC. It lasts ~7 years. As for the alarm/wake up signal, I have no idea. Does the ds3231 support that?
Get one of those DS3231 modules from ebay which have a coin cell as battery backup. I have one of those and after an year of use, the error was within a minute.
Does it support alarm/wake up signal? EDIT: I checked, it does.
Also, instead of the sparkfun esp8266 board, I think you should get a nodeMCU board.
Cool! Seems way more convenient with the USB port. However, it seems to consume much more memory in deep sleep mode: minimal power consumption seems crucial for this little foosball project. There are solutions (as explained in the blog post) but they require soldering. Wouldn't it be simpler to stick with the esp8266? Again, I'm no expert.
And I think [/url]this sensor would be a better choice.