This sentence really needs a plan to back it up.
1) Building a custom chip is not ever straightforward. I say this as someone who has designed ASICs using appropriate high-level tools such as Verilog.
2) I don't understand how one could customize a chip for browsing the web. The modern web is inseparable from JavaScript, which is a general-purpose programming language and thus requires a general-purpose CPU somewhere. At best one could integrate, say, the NIC with the processor, but this is already commonly done.
3) I fail to see how it's possible for a web browser to operate without access to RAM. Page layout involves complex algorithms which are slow. Therefore their output (graphics) must be cached, or else the user would have to wait several seconds to scroll the page. Perhaps the author means to use a very large (tens of megabytes) on-chip cache, suitable for browsing a single web page, but that would inflate the cost of the chip beyond feasibility.