Look at the last page, Figure 10. This illustrates the model he says works, and it's clearly a form of waterfall.

Sorry, but you are wrong.

The bit of fig.10 that looks like the waterfall model -- the bit to the right of the dashed line -- is simply a reiteration for contrast of fig.4, of which Royce says (in the text above fig.4):

I believe in this concept, but the implementation described above is risky and invites failure. The problem is illustrated in Figure 4. The testing phase which occurs at the end of the development cycle is the first event for which timing, storage, input/output transfers, etc., are experienced as distinguished from analyzed. These phenomena are not precisely analyzable. They are not the solutions to the standard partial differential equations of mathematical physics for instance. Yet if these phenomena fail to satisfy the various external constraints, then invariably a major redesign is required. A simple octal patch or redo of some isolated code will not fix these kinds of difficulties. The required design changes are likely to be so disruptive that the software requirements upon which the design is based and which provides the rationale for everything are violated. Either the requirements must be modified, or a substantial change in the design is required. In effect the development process has returned to the origin and one can expect up to a lO0-percent overrun in schedule and/or costs.

The bit of fig.10 to the left of the dashed line is his alternative designed to correct the flaws in the waterfall model, which with its feedback loops and iterative processes is clearly the antithesis of the (no going back; never throw anything away) waterfall model.

Instant analysis doesn't cut it here.