I watched a lot of people buy Gateway systems from the mid 1990s to ~2004, it wasn't Dell or Apple that caused Gateway's business to stall - it was quality. The product got worse and worse. Gateway did themselves in.
From what I remember, Dell did a much better job of managing supply chain costs than Gateway did. I suspect that the declining quality was Gateway cutting corners to remain price-competitive with them. It's quite possible Gateway could have maintained quality at higher prices, but that would have just been a different way to die (and quite possibly a faster one - declining quality takes more time to recognize than higher prices, plus Apple's resurgence would have complicated any plan to go after the high end). Either way, pressure from Dell is what backed Gateway into that corner in the first place, so it is entirely reasonable to attribute Gateway's problems to them.