There are several circuits on the internet from noatable sources that show how LEDs can be powered directly from an AC supply without a transformer. Here's one from ON semi: -
And here is the document it came from. The document is entitled "High Current LED - capacitive drop drive application note".
Here is another interesting article, this time from EDN. It shows the following diagram, again transformerless: -
And another article and circuit here: -
To understand how these devices function, it helps to understand how traditional LEDs function. An LED is a Light Emitting Diode, so basically you can think of it as a simple PN junction that would be used in a diode (although in actuality the structure of LEDs is more complicated, often a double heterojunction structure).
(source: gsu.edu)
Based on images of a similar LED "filament" bulb on Amazon image1, image2
It seems that each "filament" is a single LED with a radial structure, that is using radial layers rather than the traditional planar layers. So the core layer (cathode for example) would be composed of a conductor/metal, then the next outer layer would be n-type material, then the next outer layer would be p-type material, and finally the outermost layer would be a transparent conductor (to let light pass through it) such as ITO (Indium-Tin-Oxide).
It looks as though the LEDs in the bulb are arranged as two lines in parallel, each with two LEDs in series.
The driver would depend on the specs of the particular LED "filaments", but a driver could be as simple as diode bridge if the LEDs have a high enough forward voltage.
Because these LED "filaments" are so long and thin, they have a large amount of surface-area per volume, so that the heat is more dissipated than in a traditional LED.
Best Answer
The forward voltage of the LED might be higher than the test voltage of the multimeter, usualy red LEDs have the lower forward voltage and blue and white ones have the higher voltage.