Be pleased. This is a very positive feature of your character.
You need to be sure what path the sound is takling to get to your neighbours. is it really coming through the gaps around the door? it might be going directly trhough th ewalls or floors.
Anyway: Quite a lot of sound can pass though the small gaps beween the door and the door frame. When doing more structural sound isolation work they always try to 'caulk' (fill) these little gaps. You might find that some of that foam rubber strip, used for stopping draughts, would help. The gap across the bottom might be harder to fill, but even there you could lay a draught excluder 'saussage'.
If sound is going through the walls and you cannot alter the walls then simply moving your loudspeakers away form th ewall would help. Also, it helps to put the speaker close to where you sit so that overall volume can be set lower but you still get the same sound level.
Unless you are a stereo aficionado and *have* to have almost perfect timbre and quality then I suggest you have a look around some of the boot fairs or totty shops for heavy curtains and hang them from the walls you need less sound to dissipate through. Isolation of the speakers from the floor *might* help but other than that all you have left is earphones.
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