[CI] Test R package with CMake (#10087)

* [CI] Test R package with CMake

* Fix

* Fix

* Update test_r_package.py

* Fix CMake flag for R package

* Install system deps

* Fix

* Use sudo

tests/ci_build/test_r_package.py

@@ -277,6 +277,19 @@ def test_with_cmake(args: argparse.Namespace) -> None:
                     "Release",
                 ]
             )
+        elif args.compiler == "none":
+            subprocess.check_call(
+                [
+                    "cmake",
+                    os.path.pardir,
+                    "-DUSE_OPENMP=ON",
+                    "-DR_LIB=ON",
+                    "-DCMAKE_CONFIGURATION_TYPES=Release",
+                    "-G",
+                    "Unix Makefiles",
+                ]
+            )
+            subprocess.check_call(["make", "-j", "install"])
         else:
             raise ValueError("Wrong compiler")
     with DirectoryExcursion(R_PACKAGE):
@@ -333,9 +346,9 @@ if __name__ == "__main__":
     parser.add_argument(
         "--compiler",
         type=str,
-        choices=["mingw", "msvc"],
+        choices=["mingw", "msvc", "none"],
         help="Compiler used for compiling CXX code. Only relevant for windows build",
-        default="mingw",
+        default="none",
         required=False,
     )
     parser.add_argument(