Most international routes are still governed by the principles contained in the first 'bilateral air service agreement' - the agreement between the US and the UK made at Bermuda in 1946. (aka Bermuda I)
(The Chicago Convention the previous year had failed to reach any agreement on 'economic issues' and left this to States to agree these terms bilaterally. However in Chicago it was agreed that States had an exclusive right to the airspace over it's soil and no airline of another state could fly to/from or over it without a specific agreement. This meant that all airlines had to have a nationality)
Bermuda I set out the requirement that airlines possess the nationality of the those that owned it. In other words an "American" airline must be substantially owned and effectively controlled by US nationals and a "British" airline had to be substantially owned and effectively controlled by UK nationals (or the UK government).
When two governments sit down and negotiate an air service agreement the are talking about the rights to be granted to airlines of the two states - and not rights to be given to airlines of a third state. When Germany and Hong Kong talk they discuss rights to be given to German and Hong Kong airlines (HKG is a little special given their special status in China, but for the purpose of this discussion pretend that HKG is a State.) They could agree, for example that HKG airlines could fly non-stop or direct services to 5 German points, and German airlines could fly non-stop or direct services from 5 German airports. Germany could also agree to allow HKG airlines to provide services from Germany and an intermediate point (e.g. HKG-VIE-FRA with traffic rights on the VIE-FRA sector) or a beyond point (e.g. HKG-FRA-LON with traffic rights on the FRA-LON sector).
In order to actually use these '5th freedom' authorities CX would also need the agreement of Austria to carry traffic VIE-FRA and the UK to carry traffic FRA-LON. Yes it's complex.
However if a country in the middle has an agreement with Germany and with Hong Kong to carry local traffic, these can be combined to provide it's airline with connecting service via their home airport. Many years ago governments tried to regulate the prices these 6th freedom carriers could charge, but that is no longer the case. (impossible to control).
As it is very unlikely that Germany would agree with the UAE to allow their airlines to provide non-stop services between Germany and Hong Kong (or anywhere else other than the UAE) EK and EY cannot offer such services. (In any case they would also need the agreement of HKG as well.
Some ASAs now allow variation on the ownership and control rules. For example the US-EU ASA allows any EU airline to operate between US airports and any EU airport. For example AF did operate from LHR to the US for a while. However, for other reasons, this is not popular with airlines who find it difficult to make money operating these kind of routes.
In case you don't know:
1st Freedom the right to fly over a foreign country, without landing there.
2nd Freedom the right to refuel or carry out maintenance in a foreign country on the way to another country
3rd Freedom the right to fly from one's own country to another
4th Freedom the right to fly from another country to one's own
5th Freedom the right to fly between two foreign countries during flights while the flight originates or ends in one's own country.
6th Freedom the so-called right to fly from a foreign country to another one while stopping in one's own country for non-technical reasons
7th Freedom the right to fly between two foreign countries while not offering flights to one's own country
8th Freedom the right to fly between two or more airports in a foreign country while continuing service to one's own country
9th Freedom the right to fly inside a foreign country without continuing service to one's own country.
6th is 'so-called' because it is almost never mentioned in an ASA - it is taken, not given.
7th freedom is common for all-cargo operations - almost unheard of for passenger. (The AF LHR-US flights were 7th)
8th/9th exist only in principle. I'm unaware of any operations that take advantage of this today.