No, they progressed from "radio" transmission (Horizon) to "subspace" transmission, it's as simple as that.
Doesn't work even in the TOS context, where subspace transmission was available back in the old Romulan war.
Of course, the out-universe rationale for this is that TOS had piss-poor continuity. But there's no reason for the fans to add more of that drivel when the well-written spinoffs elegantly solve such problems by establishing further facts of the Trek universe.
That line of dialogue is evidendtly presented in the context of propulsion, so I'm unable to understand how this could possibly be misread.
And yet you keep misreading it.
It does not say that Romulans
do not have warp drive. It says this particular starship has "simple impulse power", whatever that is. It is impossible to read into it that Romulans do not have warp drive, because they demonstrate warp drive in the very episode (their torpedo outruns the Enterprise
Trying to say that the line refers to the capabilities of the Romulan culture is taking guesswork to a ridiculous extreme. To no avail, even, as Romulans in every other episode are fully and explicitly capable of warp, and nothing would be gained dramatically by trying to insist against all this evidence that they are not.
And yet generations of stupid fans and even misguided pro writers have insisted on Romulans being incapable of warp until, what, the Tuesday before "Enterprise
Incident"...? It's quite analogous to insisting that Klingons must be incapable of decloaking because their ships weren't seen in "Errand of Mercy", and only develop the ability to drop their cloaks for "Trouble with Tribbles".