You're getting good info. Let the chip switch a transistor, and let the transistor drive the relay.
To see why adding a resistor won't work, look at the data sheet of the relay. I can see that your SIS-2 chip is rated at about 5V. If you put a 142 ohm resistor in series with a 58 ohm relay, and then apply 5V to the series combination, then yes, your chip will see a 200 ohm load, and that load will draw 25mA.
But the relay's coil will see about 1.4V and 25 mA. Does relay's data sheet say it will trip using 25mA at 1.4V? I suspect not, but do check.
Using the transistor as a switch to drive the relay will allow you to give the relay a full 5V, or whatever your power supply rail can supply. For example, it's easy enough to drive a 12V relay with a 5V chip if you have a 12V supply rail available and you let a suitable transistor do the switching.