The majority of their satellites just bounce the signals back down to a nearby ground station. Their version 1.5 sats, which they started launching about a year ago, include laser links to allow sat->sat communication. Their plan is for the remaining 3/4th of their fleet to have laser links.
One interesting side-effect of the laser links is that they can open up connections between stock exchanges and trading houses that are faster than direct fiberoptic lines. Milliseconds count in high frequency trading.
Predictability and stability count a lot as well. I think the starlink-as-low-latency-trading-medium is sort of like "blockchain for real estate" - it's not actually a real thing.
You can simply use multiple links to send same data. The fastest one wins, so if there's a temporary hickup on one of the links, you still get somewhat bounded latency. When things work fine, you get to reap the latency benefit.
So I think it's plausible for intercontinental links.
Yeah SpaceX will have a very hard time beating the current routes; they're further from the surface and the intersatellite links won't be travelling in a straight line all the time. The best bet is if they can provide those links across oceans that can't be rigged with microwave towers.
The HF radios are transatlantic and transpacific using 10-30 MHz radios. The terrestrial microwave links (several GHz) have been around for a decade, and HF radio is fairly recent. Starlink will have higher bandwidth, but also higher latency.
One interesting side-effect of the laser links is that they can open up connections between stock exchanges and trading houses that are faster than direct fiberoptic lines. Milliseconds count in high frequency trading.