Well, shame on me for not checking, but I was on mobile, so it's not that easy.
Either way, if you wrote the model right, your DV6-3090SI has an i7 720QM, 6GB memory and an ATI HD 5650; while the the CPU is kinda on the "ok" side and RAM is more than enough for a laptop, the GPU is barely enough to play any game at high details.
You MIGHT be able to play them at low, under 720p resolution or lower, but that's that. You don't have a built-in card with that CPU, so it's strictly running on the discrete HD 5650. Your other laptop may feature an older but beefier card, which can outperform your current HP's one.