In short: you have your macro backwards.
Macros are not formed as "Take this set of commands and call it X" but "Make this macro X and have it equate to this set of commands".
Where you have:
#define Serial.println(x) DEBUG_PRINT(x)
it should instead read:
#define DEBUG_PRINT(x) Serial.println(x)
When you call it, because the macro doesn't contain a semi-colon in it, you need to specify the semi-colon as if you were calling a function:
You can omit the semi-colon only if you have a semi-colon in your macro:
#define DEBUG_PRINT(x) Serial.println(x);
By doing it that way your "empty" macro now does become truly empty when used. Without the semi-colon in the macro you would have to use:
Which for the empty variant would end up as:
Not always desirable, and can cause some problems.
So by adding the semi-colon into the macro you can omit it from the usage of the macro, and your empty variant now becomes: