Here is what I understand from Trek lore, and reading tons of trek books. (as I would guess most here have done)
The Romulan BOP was capable of faster than light travel. As was said this was a mid 1st season
episode and things were still being fleshed out.
It seems the "impulse" power vice "warp" power" referred to the ships power not the speed. The Enterprise used a matter/antimatter reaction to develop the power to generate the warp field so it could go at "warp" speed. Faster than light. The Romulan used atomic fusion power so it's warp field was much less powerful, thus a slower "warp" speed. And the cloaking device used so much power that they could not go to warp speed, faster than light, while cloaked.
While the Enterprise could go warp 6 (8 under emergency conditions) I get the impression the BOP
could only go less than warp 5. Probably much less. ( based on the NX-01 being a "warp 5" ship, it used matter/antimatter).
The Phoenix was the 1st Terran warp ship and It had no matter/antimatter in it.
Thats always what I thought/rationalized. It works for me anyway.
PS
Boy after reading my post, I'm a real geek!