Unfortunately I don't think this works:
1) You have 5 segments within Asia. You are only allowed 4 and cannot buy extra in the continent of origin.
2) Depends on your interpretation of the usual problem rule:
Code:
123N . 5. ONLY 1 INTERCONTINENTAL DEPARTURE AND 1
124N . INTERCONTINENTAL ARRIVAL PERMITTED IN EACH
125N . CONTINENT EXCEPT AS FOLLOWS:
126N . * 2 PERMITTED IN NORTH AMERICA WHEN 1 IS A
127N . TRANSIT WITHOUT STOPOVER.
128N . * 2 PERMITTED IN ASIA WHEN 1 IS A TRANSIT
129N . WITHOUT
130N . STOPOVER OR ON DIRECT SINGLE PLANE SERVICE
131N . BETWEEN THE SOUTHWEST PACIFIC AND EUROPE.
They could well argue that your second entrance into Asia is a transit without stopover between SWP and N America, rather than between SWP and Europe (on the basis that, even though they will allegedly charge you for Europe you are not actually going there).
CX's version of the rule is even more explicit:
"2. Two permitted in Asia when one is a transfer without stopover or on direct single service, between Southwest Pacific and Europe."
Aside from that I have never seen it said explicitly that this must be a 4 continents. What the CX version of the rules has to say on this is:
"Nonstop travel between DEL and CHI (ORD) is permitted.
For travel ex North America/Asia - when this service is utilised a minimum of a 3 continent fare must be charged."
So it is not inconceivable that this would still be a 3 continent fare (if you can fix the other problems above).