use Nodemcu to program Attiny85
Modifications to the ArduinoISP.ino sketch
I made the following changes to the ArduinoISP.ino file it exists in IDE version 1.8.13, and uploaded it to the NodeMCU board.
In short, I commented out (by way of #if 0) the heartbeat, err, etc LED related stuff.  Not doing this causes the board to reset for reasons that would probably be apparent if I researched it, but I haven't and since I don't plan on using the LEDs and that you may not, I figured I would get this to you sooner.
I changed RESET to be SS which on NodeMCU is D8.
Why LED related code causes resets
... Out of curiosity I just went and looked at the ESP-12F and ESP8266EX datasheets.  GPIO7, GPIO8, GPIO9 all go to the ESP-12F's SPI flash (program storage), so ostensibly monkeying with them interferes with the modules ability to keep executing from the SPI flash.  They're not routed to NodeMCU pins, probably for that reason.  So there's the answer to that.
Differences
@@ -70,7 +70,7 @@
 // The standard pin configuration.
 #ifndef ARDUINO_HOODLOADER2
 
-#define RESET     10 // Use pin 10 to reset the target rather than SS
+#define RESET     SS // Use pin 10 to reset the target rather than SS
 #define LED_HB    9
 #define LED_ERR   8
 #define LED_PMODE 7
@@ -216,15 +216,17 @@
 
 #endif
 
 void setup() {

   SERIAL.begin(BAUDRATE);
 
+#if 0
   pinMode(LED_PMODE, OUTPUT);
   pulse(LED_PMODE, 2);
   pinMode(LED_ERR, OUTPUT);
   pulse(LED_ERR, 2);
   pinMode(LED_HB, OUTPUT);
   pulse(LED_HB, 2);
+#endif
 
 }
 
@@ -276,6 +278,7 @@
 }
 
 void loop(void) {
+#if 0
   // is pmode active?
   if (pmode) {
     digitalWrite(LED_PMODE, HIGH);
@@ -291,6 +294,7 @@
 
   // light the heartbeat LED
   heartbeat();
+#endif
   if (SERIAL.available()) {
     avrisp();
   }

NodeMCU to ATTiny85 ISP Wiring
The board is wired to the ATTiny85 as follows:
NODEMCU 3.3V -&gt; ATTINY85 PIN 8
NODEMCU GND  -&gt; ATTINY85 PIN 4
NODEMCU D5   -&gt; ATTINY85 PIN 7
NODEMCU D6   -&gt; ATTINY85 PIN 6
NODEMCU D7   -&gt; ATTINY85 PIN 5
NODEMCU D8   -&gt; ATTINY85 PIN 1

On the NodeMCU you'll find all 6 of these together on the right.
Verifying AVRDUDE functioning
avrdude -P /dev/ttyUSB0 -c stk500v1 -b 19200 -p attiny85

Reading | ################################################## | 100% 0.02s

avrdude: Device signature = 0x1e930b (probably t85)

avrdude: safemode: Fuses OK (E:FF, H:DF, L:71)

avrdude done.  Thank you.

I've been playing with this chip, so don't be surprised that I don't have the same fuse values you have.