Q:

Preposition omission in an interrogative sentence

What's the correct one? Is it preposition omission? If so, could you please give me the detailed rules for it?

When will the game come to an end?
When will the game come to an end at?

A:

This is not a case of preposition omission.

When will the game end?

This is the simplest sentence that expresses the same idea.  "Come to an end" is an idiom that has the same meaning as "end" in the above example.
Grammatically, "end" is being used as an instransitive verb, which can stand on its own without a preposition.  By doing so, you are leaving the condition of ending unspecified, which is acceptable.  Here are some examples of using the intransitive verb "end."

will endhasn't endedhave ended will have endedetc.

You need a preposition when you need to specify the condition of "end."  The condition can be a time:

Shouldn't the game have ended at 2:00 p.m.?

Or it could be a rule of the game:

Shouldn't the game have ended with that last goal?

Or any other appropriate preposition:

Shouldn't the game have ended on the hill?

Thus, using your original example:

Shouldn't the game have come to an end at 2:00 p.m.?

Conclusion
Use a preposition when you need to specify a condition of the intransitive verb "end."  Don't use a preposition when it is acceptable to be unspecific.
Thus, your first example is grammatically correct.  Your second example is grammatically incorrect.

