It’s more the iGPU. You can’t really fit a dedicated GPU in a handheld form factor, so even the handhelds that came before the Steam Deck all relied on relatively pedestrian iGPUs available in Intel chips. AMD was notably missing in this area of the market, as they weren’t heavily into mobile at the time, and only had iGPUs in a few of their desktop chips, and even that came with big sacrifices to CPU performance to get. The Steam Deck came at a time when AMD was stepping up their game here, probably mostly for the next gen consoles, and were finally about to release a mobile chip with RDNA, though that was still in development. Valve had to actually get custom silicon made that backported RDNA into a Zen 2 package, because there still wasn’t anything on the market from any of the players that could actually deliver an acceptable mobile gaming experience at a reasonable power envelope for a handheld device.

It could be argued that that is actually still the case, as AMD is still mostly focused on the laptop market with its mobile APUs. The Z1 and Z1 Extreme are laptop chips, which is why they target a 30W TDP (laptops, being larger, inherently have bigger batteries to support it). Handhelds like the Ally just started popping them into their devices to claim better performance, but that’s why their battery life is ass. Even pulling those chips back to 15W TDPs like the Steam Deck doesn’t fix the battery problems or offer even significantly better performance than the Steam Deck, despite the newer CPU and GPU architectures. A chip specced for 30W is just inherently more inefficient than one specced for 15W, regardless how much of the power you’re actually using. This is why Valve says the tech for a Steam Deck 2 doesn’t exist, yet. They aren’t willing to compromise the Steam Deck being a truly portable handheld, and you can’t deliver that currently.