Not all scopes that can display digital information on their screens are DSOs.
A Digital Storage Oscilloscope, by definition, digitizes an analog signal, stores those digitized samples, and then displays it. DSOs could be constructed with LCDs, CRTs, or any other display technology--there are even DSOs that don't have any display at all, and rely on being connected to a PC to display captured data. So if there's no digitizing, and no storage, it's not a DSO.
It is this storage that provides the DSO the ability to perform arbitrary computations on the captured waveform, whether FFT, or integration, or whatever. But just displaying text on the CRT does not mean you have a DSO on your hands.
The sort of thing you see in the picture in the OP is actually not uncommon in analog 'scopes, especially later models. Essentially the CRT can be driven by the analog front end, where the horizontal position is controlled by a ramp generator (the horizontal timebase) and the vertical position is controlled by the channel amplifier, or it can be controlled by perhaps a small microprocessor to draw vector shapes, as you would see in a vector monitor. Essentially, the scope alternates between drawing waveforms and drawing informational text or other information on the screen, presumably doing the vector drawings in between triggers.
Some analog CRT scopes could even take digital measurements of voltage or time, with cursor position readouts and text menus that could be displayed and navigated through. However, it wasn't very long after that when DSOs became viable, and quickly took over the market.