Как вывести подтверждения закрытия окна PyQt

Я не совсем уверен, что правильно понимаю то, что вы хотите сделать. Но попробуйте так:

import sys
from PyQt5 import QtCore, QtGui, QtWidgets
# ???from openpyxl import load_workbook


class Ui_closewindow(object):
    def setupUi(self, closewindow):
        closewindow.setObjectName("closewindow")
        closewindow.setFixedSize(716, 269)
        closewindow.setStyleSheet("background-color: rgb(184, 234, 255);")
        self.question_close = QtWidgets.QLabel(closewindow)
        self.question_close.setGeometry(QtCore.QRect(0, 0, 721, 71))
        self.question_close.setStyleSheet("color: rgb(255, 255, 255);\n"
"font: 24pt \"MS Shell Dlg 2\";\n"
"background-color: #00bbf9;")
        self.question_close.setAlignment(QtCore.Qt.AlignCenter)
        self.question_close.setObjectName("question_close")
        self.closethegamebtn = QtWidgets.QPushButton(closewindow)
        self.closethegamebtn.setGeometry(QtCore.QRect(160, 130, 171, 61))
        self.closethegamebtn.setStyleSheet("QPushButton{\n"
"border:none;\n"
"background-color: rgb(255, 174, 75);\n"
"font: 28px \"MS Shell Dlg 2\";\n"
"color: white;\n"
"border-radius: 10px\n"
"}\n"
"QPushButton:hover{\n"
"border:none;\n"
"background-color: rgb(255, 0, 127);\n"
"font: 28px \"MS Shell Dlg 2\";\n"
"color: white;\n"
"border-radius: 10px\n"
"}")
        self.closethegamebtn.setObjectName("closethegamebtn")
        self.donotclosethegamebtn = QtWidgets.QPushButton(closewindow)
        self.donotclosethegamebtn.setGeometry(QtCore.QRect(390, 130, 171, 61))
        self.donotclosethegamebtn.setStyleSheet("QPushButton{\n"
"border:none;\n"
"background-color: rgb(255, 174, 75);\n"
"font: 28px \"MS Shell Dlg 2\";\n"
"color: white;\n"
"border-radius: 10px\n"
"}\n"
"QPushButton:hover{\n"
"border:none;\n"
"background-color: rgb(255, 0, 127);\n"
"font: 28px \"MS Shell Dlg 2\";\n"
"color: white;\n"
"border-radius: 10px\n"
"}")
        self.donotclosethegamebtn.setObjectName("donotclosethegamebtn")
            
        self.retranslateUi(closewindow)
        QtCore.QMetaObject.connectSlotsByName(closewindow)

    def retranslateUi(self, closewindow):
        _translate = QtCore.QCoreApplication.translate
        closewindow.setWindowTitle(_translate("closewindow", "Close"))
        self.question_close.setText(_translate("closewindow", "Naozaj chcete hru uzavrieť ?"))
        self.closethegamebtn.setText(_translate("closewindow", "Ano"))
        self.donotclosethegamebtn.setText(_translate("closewindow", "Nie"))


class CloseWindowClass(QtWidgets.QWidget, Ui_closewindow):
    signalCllose = QtCore.pyqtSignal(bool)                        # !!! +++

    def __init__(self, parent=None):
        super().__init__()
        self.setupUi(self)
        
        self.setWindowFlags(QtCore.Qt.WindowStaysOnTopHint)       # !!! +++
        self.flag_close = False                                   # !!! +++
        
        self.setWindowIcon(QtGui.QIcon('icons/close.svg'))
        self.parent = parent
        self.donotclosethegamebtn.setCursor(
            QtGui.QCursor(QtCore.Qt.PointingHandCursor))
        self.closethegamebtn.setCursor(
            QtGui.QCursor(QtCore.Qt.PointingHandCursor))

        self.donotclosethegamebtn.clicked.connect(self.hide)
        self.closethegamebtn.clicked.connect(self.cl)

    def cl(self):
        self.flag_close = True                                   # !!! +++
        self.signalCllose.emit(True)                             # !!! +++
        

class Ui_Gamepol(object):
    def setupUi(self, Gamepol):
        Gamepol.setObjectName("Gamepol")
        Gamepol.setFixedSize(777, 600)
        

class MainWindow(QtWidgets.QMainWindow, Ui_Gamepol):
    def __init__(self):
        super().__init__()
        self.setupUi(self)
        
        self.window = CloseWindowClass()                             # !!! +++
        self.window.signalCllose.connect(self.close)                 # !!! +++

# !!! vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv
    def closeEvent(self, event):  
        self.window.show()
        if self.window.flag_close:
            self.window.close()
            event.accept()
        else:
            event.ignore()
            

if __name__ == "__main__":
    import sys
    
    app = QtWidgets.QApplication(sys.argv)
    window = MainWindow()
    window.show()
    sys.exit(app.exec_())