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The Maximum Display Resolution for the 2nd Generation Intel® Core™ Processor Graphics (HD Graphics) is 1920x1080 via HDMI/VGA only. Keep in mind that the resolution you are trying to set can only be done by using DisplayPort*. In this case, the motherboard in your laptop limits the maximum resolution up to 1920x1080 by not supporting DisplayPort*.
Ok, so I have managed to make it work by adding a custom resolution in Intel Graphics and Media Control Panel's Advanced Mode (right click on desktop -> Graphics Properties... -> Advanced Mode -> Custom Resolutions under Display menu). The parameters that worked for me in the end are 2560 x 1440, 55 Hz refresh rate, 32 bit color depth, and CVT-RB timing standard. Don't know why my previous trials didn't work, I probably didn't set a correct combination of parameters. BTW this article was helpful regarding the topic: 2560x1440 or 2560x1600 via HDMI - NotebookCheck.net Tech