I assume this rocket is not a part of some orbital program. It's more like the SpaceX's Hopper [1], intended to test the control algorithms and such.
A booster / orbital vehicle, when it appears, should have very different characteristics. I can even imagine that some kind of compatibility standard may arise, allowing to stack custom orbital vehicles to reusable boosters, much like the standardized buses for smaller satellites that exist today.
> "competition leaped directly to testing an engine they were developing for orbital launches"
SpaceX' Starhopper was an orbital Raptor engine. The *test vehicle* wasn't orbital, but, it's testing the in-development orbital engine and associated plumbing under flight conditions (which is useful, because... well you can see the various ways Starhopper failed at the start). Likewise, Grasshopper before that, in 2012-3, was a single Merlin engine (the Falcon 9 has, eponymously, 9).
SpaceX never flew a suborbital hop with anything other than an engine intended for orbital flight.
I think if Honda had an orbital-class reusable engine at the hardware stage, that'd be flying that to test it as much as possible. I'm not aware of any of the competitors doing otherwise. This is signalling they don't (yet?) have one.
edit: Or LandSpace, whose 10 km suborbital hop last year flew one of the methane engines their orbital vehicle has nine of.
From the press release: «Honda rocket research is still in the fundamental research phase, and no decisions have been made regarding commercialization of these rocket technologies». It also has no mention of the engine used. Honda indeed appear to not have an engine worth noticing yet.
A booster / orbital vehicle, when it appears, should have very different characteristics. I can even imagine that some kind of compatibility standard may arise, allowing to stack custom orbital vehicles to reusable boosters, much like the standardized buses for smaller satellites that exist today.
[1]: https://starship-spacex.fandom.com/wiki/Starhopper