As it says on the BOM, the kits with red LEDs actually have 220 ohm resistors; the “200 ohm” figure was a preliminary estimate.
The number that you need to be concerned about is normally the total current on the MCU, which needs to be 200 mA or less. That gives you nearly 40 mA (for one IR LED) plus a little under 8*20 mA for the 8 visible LEDs, plus a few mA to run the MCU. With the standard component set, it runs pretty close to the limit.
