... some insight on what the output transformer does and how the tubes in this case might replace it.
ok, I'll try for a brief explanation, amp experts please don't berate me if I oversimplify this ...
In a standard amplifier with an output transformer, the valves need to work into a high impedance (AC resistance) load. Where your speaker load is between 4 and 16 ohms, the output tubes need a load of something like 6 kiloohms. Although most people are familiar with transformers as voltage converters they also transform - or more technically "reflect" - impedance. This means that an impedance connected across the output terminals appears to be a different impedance on the input terminals.
Long story short, it's to do with the transformer's turns ratio, the number of turns of wire on the primary winding (where the output tubes are connected) to the number of turns of wire on the secondary (where the speaker is connected).
Suppose the ratio is 20:1. The impedance ratio of a transformer is the square of the turns ratio so in this case 400:1. That means that a 16 ohm load on the secondary appears as a 6400 ohm load on the primary.
Additionally, the output transformer isolates the speaker from the high voltage DC present in the amp.
OTL amps - Output TransformerLess - rely on a different power amp design, usually taking the output from the cathodes rather than the anodes of the output tubes. This type of design does not require as high an impedance load as normal amps but does not generate as much output power.