The first point below is based on how the bidding might have gone had East opened the bidding as they were entitled to. The second point is based on the actual scenario that occurred.
Point 1 – The very easy answer is that dealer EAST is quite entitled to open the bidding and this makes life much simpler for West and difficult for that pesky South to throw a spanner in the works!
East has a justifiable bid using the “Rule of 20” which takes into account that very important aspect in bridge of the Power of Shape. The Rule of 20 for opening means that when your HCP (10 in this case), plus the length of your 2 longest suits (6 D plus 4 S = 10), giving you the required 20 to meet the Rule of 20, then you should treat this as an opening hand.
Note: If you play “losing trick count” you only have 6 losers which is also worth an opening hand.
East opens its longest suit; ie. 1 Diamond (note – definitely not 2D as the hand is too strong for a weak 2D bid).
This makes it difficult for South who not having a 5 card suit for a legitimate overcall, can only double showing opening hand values.
West will probably go 2 Clubs; East repeats Diamonds; West shows Hearts; East shows Spades, then West will go 3NT but because of Easts shape, East should repeat Diamonds again and West must go to at least game in D with the top 2 and might even be tempted to look for a D slam if brave.
Point 2 - Because there was no opening bid from East, things are more difficult to judge for West.
The Double by West is best to show a particularly strong hand. (North should stay completely silent through the auction).
East can to some extent make up for their lack of an original opening bid by quite justifiably bidding 2 Diamonds (ie. a jump) which logically shows good suit quality (at least 5 in the suit, probably 6) and 9 to 11 HCP.
Being a passed hand already, West should know that partner has not a big hand but one that was close to opening!
A wise South seeing all this (and vulnerable!) should then pass, otherwise a penalty double by E/W could take South to the cleaners!
East’s actual response of just 1D to West’s double is just too timid with this hand so a jump, when not opening originally, logically shows the next best thing just below an opening.
Then E/W should find at least a very good 5 Diamond contract and if really brave a good slam in Diamonds based on shape.
With good bidding by E/W South, apart from doubling, is not really going to be able to get in nuisance bids. In fact the double from South, if East opens, more or less shows where all the missing points are thus making it easier for E/W to play their cards and make 6 Diamonds, whether in 5 or 6.