To my way of thinking, "for this time long" can be replaced by "during this period of time".
Agreed. Not only can it be, it needs to be because "for this time long" is not English.
The rest of the original sentence is butchery. Try this:
The key fob will remember any sequence of button presses that occurs during the period of time (or interval) that the LED is blinking.
Successful programming of the RX-4MHCS is confirmed by the LED with a steady red light. Afterwards it switches off.
The person who wrote that manual just loves run-on sentences.