Can this laptop work better for Elgato HD60 screen capture?
Nothing you can do, your laptop isn't made to stream.
I'd guess that if it would work with the i-3 the site wouldn't have said i-5 was the minimum.
Desktop would be better, but without a list of what is loaded on power up, and what else is being run during the screen capture, and what levels of resolution and color complexity and game settings are being sent to the Elgato, no way to guess if the i3 CPU could keep up. Many times RAM will let you run more complexity, but I doubt this is the case for your streaming. It is a matter of throughput and CPU cycles rather than holding more temp results in RAM.