と言われるゆえんである - How to parse this sentence?

Question

This is the description of one the tournaments conducted in 宝蔵院 in a videogame:

世の武芸者の基礎鍛錬を趣旨とした宝蔵院最古の闘技。
誰でも参加可能な所が宝蔵院の登竜門と言われるゆえんである。

My initial translation would be:

Houzouin's oldest contest with the aim of allowing practitioners of martial arts from all over the world to hone the basics. The fact that anybody can participate is what is said to be Houzouin's gateway to success.

I'm having lots of trouble properly parsing the second sentence.

First off, how does と言われるゆえん work here? I've googled ゆえん and found that it's an old expression meaning 理由 (seemingly interchangeable), e.g. in following sentence:

この学校が名門校だと言われる所以は、数々の有名な卒業生たちにある。
The reason that this school is said to be prestigious is due to the many famous people that have graduated from here. (this is my own translation)

But I can't for the life of me piece together what ゆえん in my sentence is actually referring to.

Second, what does 登竜門 here refer to? I understand it means gateway to success but does it refer to 宝蔵院, saying that the reason the school got so successful is due to the fact that anyone can participate or does it refer to the 武芸者, that it can be a gateway to success to anybody who wants to participate?

If somebody could break down the second sentence for me, I'd be very much obliged. Thanks!

Edit: Upon further thought, if I broke the second sentence down into the following:

誰でも参加可能な所が［宝蔵院の］登竜門と言われる理由だ。
The fact that anyone can participate is the reason why it (宝蔵院最古の闘技) is called the gateway to success (at Houzouin).

Does that make sense?

Answer 1

First off, how does と言われるゆえん work here? I've googled ゆえん and found that it's an old expression meaning 理由 (seemingly interchangeable)

Yes, you are correct. ゆえん is a Classical set phrase that literally meant "because" and now used as a formal replacement for 理由 or わけ. Due to its etymology, the word is most naturally attached to verbs.

Second, what does 登竜門 here refer to?

The word 登竜門 comes from an episode in a Chinese chronicle, that there is a waterfall where a carp can become a dragon when it has climbed to the top. Thus, it is used in a figurative sense that "a place of trial where a previously unknown person will be recognized for their ability once passed". This is why 誰でも参加可能 is a valid description for 登竜門.

Lastly, の following 宝蔵院 is actually が in a relative clause: How does the の work in 「日本人の知らない日本語」?

誰でも参加可能な所が宝蔵院の登竜門と言われるゆえんである。
"The fact that it opens to anyone is the reason 宝蔵院 is called the 'gateway to fame [as a fighter(?)]'"