It depends on your video drivers and if they support custom resolutions, but you can sometimes force higher resolutions on a smaller screen. It depends on if the video card supports the resolution, but if it does and it's just the screen that can't support it, you can normally force it to. It won't look great, but it will work for things like Conquer. Just remember to keep the aspect ratio correct.
For me, I use NVIDIA, and I can create custom resolutions for my screen (as you can see below in the first image). Some graphic drivers allow you to edit the resolution from the Windows resolution settings panel. Mine doesn't, it forces you go to through NVIDIA's custom tools, but it would appear in image two if it did.
If you can't force resolution, then you need a better laptop. That's the bottom line. Cheers.