I don't think you can use a single cloud token for 2 programs, I think you need 2 tokens.

#define REMOTEXY_MODE__ESP32CORE_WIFI_CLOUD
#include <WiFi.h>

#include <RemoteXY.h>

// RemoteXY connection settings
#define REMOTEXY_WIFI_SSID "************"
#define REMOTEXY_WIFI_PASSWORD "************"
#define REMOTEXY_CLOUD_SERVER "cloud.remotexy.com"
#define REMOTEXY_CLOUD_PORT 6376
#define REMOTEXY_CLOUD_TOKEN "********************************"

// RemoteXY configurate 
#pragma pack(push, 1)
uint8_t RemoteXY_CONF[] =
  { 255,4,0,0,0,81,0,10,13,4,
  131,1,5,18,23,9,1,2,31,83,
  116,111,114,101,32,49,0,131,0,5,
  34,23,9,2,2,31,83,116,111,114,
  101,32,50,0,1,0,44,23,15,15,
  1,2,31,88,0,1,0,65,23,15,
  15,1,2,31,88,0,1,0,44,23,
  15,15,2,2,31,88,0,1,0,65,
  23,15,15,2,2,31,88,0 };
 
// this structure defines all the variables and events of your control interface
struct {

    // input variables
  uint8_t DW_1; // =1 if button pressed, else =0
  uint8_t UP_1; // =1 if button pressed, else =0
  uint8_t DW_2; // =1 if button pressed, else =0
  uint8_t UP_2; // =1 if button pressed, else =0

    // other variable
  uint8_t connect_flag;  // =1 if wire connected, else =0

} RemoteXY;
#pragma pack(pop)

#define PIN_DW_1 13
#define PIN_UP_1 12
#define PIN_DW_2 14
#define PIN_UP_2 27

void setup()
{
  RemoteXY_Init ();
 
  pinMode (PIN_DW_1, OUTPUT);
  pinMode (PIN_UP_1, OUTPUT);
  pinMode (PIN_DW_2, OUTPUT);
  pinMode (PIN_UP_2, OUTPUT);
}

void loop()
{
  RemoteXY_Handler ();
 
  digitalWrite(PIN_DW_1, (RemoteXY.DW_1==0)?LOW:HIGH);
  digitalWrite(PIN_UP_1, (RemoteXY.UP_1==0)?LOW:HIGH);
  digitalWrite(PIN_DW_2, (RemoteXY.DW_2==0)?LOW:HIGH);
  digitalWrite(PIN_UP_2, (RemoteXY.UP_2==0)?LOW:HIGH);
}