Try the test yourself - take a big loudpeaker, face it upwards and place a house brick gently on the cone. Hook it up to your stereo and turn the volume up. If the brick moves you have proven it will work.
The principle of voice coil actuators is used widely, in fact the hard disk in your computer uses one to position the heads, it's that you might hear as a rattling inside your computer when you access a file. What matters is the scale, the coil requires more power to move a greater mass. In a solenoid, the mass is usually a metalic rod, block or ring which in relative terms is quite heavy and therefore needs a lot of 'push'. The power has to come from your audio signal so depending on size, it could need a considerable sized amplifier, possibly several hundred Watts. The power needed is dependant on the mass and the speed you move it, the faster it moves the more power it needs.
If all you want to do is tap "woody woodpecker" on a surface, it is fairly easy, if you want to reproduce the audio you have to consider that above maybe 10 taps per second, you either need a very low mass solenoid, a very short movement or a very high power. Even in the video you will notice the amount of movement is considerably less as the speed increases. It is possible to maintain the 'stroke' length at higher frequencies but only by dramatically increasing the power levels. In the one shown, to get full stroke at the highest frequency they use (~500Hz at a guess) would need forced air cooling, maybe even liquid cooling due to the high temperatures the losses and air friction would create.
The other point mentioned earlier is a solenoid moves according to absolute current through it, in other words it moves the same way regardless of the polarity of voltage you place across it. Your audio will almost certainly be AC which means it's polarity reverses during each cycle of sound. If you want to hear some semblance of the audio quality, by that I mean the audio should be recognizable if it was voice or music, you have to apply a bias to it. It means instead of the audio directly driving the solenoid, you use it to modulate a fixed 'push' already on it. That allows you to increase or reduce the effect of the fixed 'push' and gives a more linear movement relative to the audio you apply. The fixed bias can be mechanical, using a spring mechanism, magnetic, using a fixed attraction or repulsion of magnets or by passing a fixed current through the solenoid as well as the audio.
Brian.