Please don't include information about the Story Format being used within the Question Title, it just makes it longer than necessary. There are a couple of issues with your example:
1. You have a number of Data-Type miss-matches.
You are initialising the $Mode story variable as an Array, you have the <<radiobutton>> macros are assigning String values, and you are checking for Numeric (Integer) values in the conditional expressions of your <<if>> related macro calls.
I suggest changing each of those three things to use the same data-type, a Numeric (Integer) value perhaps.
2. The 2nd <<radiobutton>> macro is malformed.
You should using a Space character to separate the checked keyword from the checkedValue value.
3. Using the value assigned by the <<radiobutton> macros within the same Passage it's set in.
The contents of the whole Passage is processed before it is show to the Reader, this means that your <<if>> related macros are processed before the Reader has had a chance to select one of the <<radiobuttons>>.
The standard way to over come this issue is to place the <<if>> related macros on the next Passage shown to the Reader.
4. You are passing a conditional expression to your <<else>> macro, that macro doesn't accept a parameter.
5. You are using the deprecated <<display>> macro to display the contents of your Easy, Normal, and Hard passages.
You should be using the replacement <<include> macro instead.
The following is a slightly modifies version of your own example, it is written using TWEE Notation and consists of two Passages named Start and Result
<<set $Mode to 2>>
<<radiobutton "$Mode" 1>><span style="color:#008000">''Easy''</span>.
<<radiobutton "$Mode" 2 checked>><span style="color:#FFFF00;">''Normal''</span>.
<<radiobutton "$Mode" 3>><span style="color:#FF0000;">''Hard''</span>.
<<if $Mode is 1>>
<<elseif $Mode is 2>>