Why does using ESP8266 in deep sleep mode still drain the battery quickly?
The example shows a Sparkfun Thing, which the article notes doesn't have extra peripherals. What you show is something different, like a NodeMCU dev board, which typically has a linear regulator, possibly a power LED (which the article notes can be removed).

I see you're using a DHT11 or DHT22, which has a pull-up resistor. The pull-up resistor is constantly using power. Instead of connecting the pull-up to the power rail, you can connect it to a GPIO pin and pull that pin LOW before you go into sleep, which effectively disables the sensor and stops it from drawing power just to keep the data line high.

Safe to say that somewhere there is something drawing power -- have you measured the actual current draw in deep-sleep, or are you only noting that your batteries run low sooner than expected?