custom-mode-base.js

// This only defines high-level behaviour of the Mode like folding etc.
ace.define('ace/mode/custom', ['require', 'exports', 'ace/lib/oop', 'ace/mode/text', 'ace/mode/custom_highlight_rules'], (acequire, exports) => {
  const oop = acequire('ace/lib/oop');
  const TextMode = acequire('ace/mode/text').Mode;
  const CustomHighlightRules = acequire('ace/mode/custom_highlight_rules').CustomHighlightRules;

  oop.inherits(Mode, TextMode); // ACE's way of doing inheritance

  exports.Mode = Mode; // eslint-disable-line no-param-reassign
});

// This is where we really create the highlighting rules
ace.define('ace/mode/custom_highlight_rules', ['require', 'exports', 'ace/lib/oop', 'ace/mode/text_highlight_rules'], (acequire, exports) => {
  const oop = acequire('ace/lib/oop');
  const TextHighlightRules = acequire('ace/mode/text_highlight_rules').TextHighlightRules;

  const CustomHighlightRules = function CustomHighlightRules() {
    this.$rules = new TextHighlightRules().getRules(); // Use Text's rules as a base
  };

  oop.inherits(CustomHighlightRules, TextHighlightRules);

  exports.CustomHighlightRules = CustomHighlightRules;
});

I wonder why you're not getting "acequire is not defined" errors, cause I certainly am.

Mode is not defined on line 7

There is a missing step where the CustomHighlighter has to be set for the Mode

let Mode = function() {
  // this ensures that all your highlight rules are set for your custom mode
  this.HighlightRules = CustomHighlightRules;
}

oop.inherits(Mode, TextMode); // ACE's way of doing inheritance

The custom mode will otherwise not have any highlight rules.

Worth pointing out, that is a part of an article on writing custom highlight rules