In a set of LED lamps powered from a 120VAC source there does NOT need to be any transformer, so its LACK proves nothing. A SINGLE LED diode will have to be supplied with a DC supply, typically in the range 3 to 6 VDC. For a SERIES string of such single LED's, that DC power supply unit is designed to supply to the STRING as a whole a DC Voltage sufficient to give the proper DC Voltage drop across EACH LED in the string. For example, a power supply module with an input of 120 VAC could output 100 VDC to a string of 20 individual LED's, each of which gets a 5 VDC supply across it. That would suffice for lamps with a small light output per LED lamp. If these are small LED's that each consume 0.5W of power (10 W total for the string), the solid state power supply circuit is relatively simple and can be done with no transformer.
What about MORE light output per lamp? The simplest is to manufacture with a string of SEVERAL LED's in one small strip and that unit is mounted in a lamp bulb (for protection, not for vacuum as an incandescent is) with the power supply module in the lamp base. A single strip of LEDs like that in one lamp is the same as as strip of individually mounted single LED's like a tree light strip. If you need more light output (using the same type of LED) you can simply mount several such strips into one bulb envelope, with each strip connected in parallel to that same DC supply. If you have looked closely at CLEAR lamps for use in 120 VAC common fixtures with LED elements, you will see those several strips (often 3 or 4) of tiny square elements. Again, even for 25W power consumption the power supply circuit is small with no transformer and fits into the lamp base. Today a typical 25W LED lamp will produce enough light to be labelled as "150W Equivalent".
NOTE here that those "more output" individual lamps with MANY LED's are the type commonly sold for use in our "regular" lamp sockets in place of older incandescent lamps and include a power supply module in EACH lamp device. These ARE designed to fit into single-lamp sockets fed from 120 VAC supply lines, so they always are connected in PARALLEL to the supply. BUT within each lamp, each small SERIES string of tiny LED's MIGHT fail due to the failure of ONE LED chip, but any other strips in parallel would still function. I note also that it appears to me that most such lamps fail NOT because to LED failure inside, but because elements of the solid state DC power supply module in the lamp base fail.
But back to the simplest set of "Christmas tree light string". The older incandescent lamp sets were designed with just the right number of small lamps in series to work on a total 120 VAC supply. For example, a string might have 50 lamps rated for 2.5 VAC each (125 VAC total). A 100 lamp set actually is two such 50-lamp sets wired together in parallel from the 120 VAC supply. If you look closely at the 50-lamp string it has two wires running along it, but connections to each lamp socket are ONLY to ONE of those wires so the sockets are all in series. The other wire runs untouched from the plug to the far end of the string where it IS connected to the LAST lamp socket. There BOTH wires also are connected to a female standard outlet socket so you can connect several strings together from one wall outlet. Because of the series connections of all lamps, failure of ONE means that entire string goes "dead". For that reason more modern lamps are made with small "shunt resistors" in parallel with each lamp's filament. That resistor does NOT provide light but DOES allow the proper current flow through, so the failure of ONE such lamp means that only that lamp will go "dead" while the rest of the series string still lights. You can buy replacement lamps for this type (getting rarer!) because failure necessitating replacement is VERY common.
The newer LED Christmas tree light strings are different because you cannot run them on AC. But they do consume very little power so each such string has a very small Power Supply circuit built into its power cord plug. Again there are two wires running the length of the string - one connecting through each lamp socket in series, and a second running undisturbed to the far end to connect to the last socket. BUT there is also a THIRD wire. That one is simply to carry the original 120 VAC supply from the source plug to the end-of-string female outlet plug (along with use of the undisturbed wire) to make such power available to the NEXT string on your tree. MOST such strings do NOT contain replaceable lamps because makers have not standardized such, and do NOT expect frequent failures requiring lamp replacement. Whole string replacement is the plan.
So, any string of low-power lights can be made with LED's as a SERIES circuit of DC lamps without tell-tale transformers or bulky obvious power supply modules. However, mindless1 above makes a GOOD point. That is NOT the only way, and I may be wrong on this caution. It IS possible that the light string OP has bought is made with PARALLEL connections to the full 120 VAC supply along the entire light string, and indivdual power supply modules built into each lamp base. The lamps here are suffuciently unique (both electrically and in appearance) to warrant having a few spares supplied with the set. mindless1 is correct to suggest, "it seems like they could still want to advertise that if one lamp burns out, the rest still work, even if they were all in parallel, because it's still true. It would be a marketing angle rather than a scientific necessity." Those lamps may even be designed with "normal" bases that fit our common light fixtures. If that is the case, shortening the string is NOT a problem.