If you have a look at the voltage/current curve for the output (fig 8 of this datasheet
https://www.ti.com/lit/ds/symlink/cd4026b.pdf) you will see that the outputs won't give more than about 20 mA with a 10 V supply and the outputs shorted.
You won't get 27 mA with the 9 V supply. There is the voltage drop across the LED and the voltage drop across the IC to consider. I don't know where you get the figure of 200 mW from.
With a 2 V LED and a 330 Ohm resistor you will get about 12 mA. There will be about 2 V drop across the LED, about 4 V drop across the resistor and about 3 V drop across the IC. That will give around 36 mW of heat in the IC. There are 7 segments, with between 2 and 6 segments lit at any one time. That is 72 mW to 216 mW depending on the digit shown.
That should be OK but the IC will be getting hot. The IC is rated to 500 mW, but that is with a junction temperature of around 150 deg C so I will be really hot to the touch.
As Nigel says, all the application circuits show a transistor between each output and the display.
The CD4026 dates back to the 1970s. The data sheet shows filament, Nixie tube and vacuum fluorescent 7 segment displays, all of which are long gone.