diff --git a/src/rules/no-default-export.js b/src/rules/no-default-export.js
index fcb4f1b2f..d1aab1248 100644
--- a/src/rules/no-default-export.js
+++ b/src/rules/no-default-export.js
@@ -15,7 +15,10 @@ module.exports = {
 
   create(context) {
     // ignore non-modules
-    if (context.parserOptions.sourceType !== 'module') {
+    if (
+      context.parserOptions.sourceType !== 'module'
+      && (!context.languageOptions || context.languageOptions.sourceType !== 'module')
+    ) {
       return {};
     }
 
diff --git a/src/rules/no-named-export.js b/src/rules/no-named-export.js
index efaf9dc4c..7a29ca01d 100644
--- a/src/rules/no-named-export.js
+++ b/src/rules/no-named-export.js
@@ -13,7 +13,10 @@ module.exports = {
 
   create(context) {
     // ignore non-modules
-    if (context.parserOptions.sourceType !== 'module') {
+    if (
+      context.parserOptions.sourceType !== 'module'
+      && (!context.languageOptions || context.languageOptions.sourceType !== 'module')
+    ) {
       return {};
     }
 
diff --git a/src/rules/unambiguous.js b/src/rules/unambiguous.js
index 91152ea2a..568802716 100644
--- a/src/rules/unambiguous.js
+++ b/src/rules/unambiguous.js
@@ -19,7 +19,10 @@ module.exports = {
 
   create(context) {
     // ignore non-modules
-    if (context.parserOptions.sourceType !== 'module') {
+    if (
+      context.parserOptions.sourceType !== 'module'
+      && (!context.languageOptions || context.languageOptions.sourceType !== 'module')
+    ) {
       return {};
     }