...this is obviously performing a 'string' comparison

No - if the date/time format matches the supported format, MySQL performs implicit conversion to convert the value to a DATETIME, based on the column it is being compared to. Same thing happens with:

WHERE int_column = '1'

...where the string value of "1" is converted to an INTeger because int_column's data type is INT, not CHAR/VARCHAR/TEXT.

If you want to explicitly convert the string to a DATETIME, the STR_TO_DATE function would be the best choice:

WHERE expires_at <= STR_TO_DATE('2010-10-15 10:00:00', '%Y-%m-%d %H:%i:%s')

But this is obviously performing a 'string' comparison

No. The string will be automatically cast into a DATETIME value.

See 11.2. Type Conversion in Expression Evaluation.

When an operator is used with operands of different types, type conversion occurs to make the operands compatible. Some conversions occur implicitly. For example, MySQL automatically converts numbers to strings as necessary, and vice versa.