The Łukasiewicz Research Network Institute of Aviation has done a test launch of a small rocket powered by a RDE using liquid fuels (propane and nitrous oxide), demonstrating that it's at least feasible to get T/W greater than 1. This was not a long flight, burning for 3.2 s and reaching only 450 m. It's not apparent if this was a limit due to the amount of propellant it could lift, the duration it could fire for, or if it was just kept short for test purposes.
The aerospike form factor is likely because the combustion chamber itself is toroidal, with detonation waves rotating around it. It's not obvious how it would work with a conventional nozzle. The combustion process involves a large, brief spike in pressure as each detonation wave passes, which the combustion chamber must be constructed to withstand. This will come with a mass penalty of some degree. Cooling should be easier, as the combustion in any given section is intermittent, but the same intermittency means thrust is likely much lower than for a similar-sized conventional engine.
In short, I would not expect these to have terribly high T/W ratios, making them poorly suited to SSTOs. These are probably better suited for high efficiency upper stage engines, where the relatively heavy combustion chamber and nozzle can be offset by using a smaller, lower thrust engine.