Arduino Lightsaber

Here you go. I took your code and simplified it. The program will play playlist zero every 5 seconds.

/***********************************
WT588D One Line Serial Demo

Plays playlist 0 every 5 seconds.

JakeSoft 2015
***********************************/

#define WT588D_SDA 4 //Connect to WT588D Pin #10
#define WT588D_BUSY 7 //Connect to WT588D Pin #15

void WT588D_Send_Command(byte addr) {
    digitalWrite(WT588D_SDA, LOW);
    delay(5);

    for(int i = 0; i < 8; i++)  {
        digitalWrite(WT588D_SDA, HIGH);
        if(bitRead(addr, i)) {
            delayMicroseconds(600);
            digitalWrite(WT588D_SDA, LOW);
            delayMicroseconds(200);
        } else {
            delayMicroseconds(200);
            digitalWrite(WT588D_SDA, LOW);
            delayMicroseconds(600);
        }
    }

    digitalWrite(WT588D_SDA, HIGH);
    delay(100);
}

void setup() {
  pinMode(WT588D_SDA, OUTPUT);
  pinMode(WT588D_BUSY, INPUT); 

  digitalWrite(WT588D_SDA, HIGH);
}

void loop()
{

  //Begin playlist 0
  WT588D_Send_Command(0);
  
  delay(5000);
}

I used arduino pins 4 and 7, but you can use whatever you want.

One other thing to check for is to make sure that you have the right processor selected in your Arduino IDE. I'm using the 8 Mhz version but it defaults to the 16Mhz version of you just select "Pro or ProMini" from the board menu. If you have the wrong processor selected then your timings will all be off and it won't work.