He traveled for Hajj but he died before Hajj began. Is he regarded as a hajji?

If a man resolves to do Hajj then dies, he must have died
either before entering ihraam or after. 

If he died before entering ihraam, then Allaah will reward
him according to his intention, but the obligatory Hajj of Islam should be
performed on his behalf.  

If he died after entering ihraam, he will have the reward of
Hajj, and he will be raised on the Day of Resurrection reciting the
Talbiyah. Therefore Hajj should not be performed on his behalf. 

Shaykh Ibn ‘Uthaymeen (may Allaah have mercy on him) was
asked about a person who saved money to go for Hajj, but died before he was
able to do so. He replied: 

With regard to this man who resolved to do Hajj and sold all
he had in order to go for Hajj, but died before he could perform Hajj, we
hope that Allaah will record the reward of the pilgrims for him, because he
intended to do a good deed, and he did what he could to prepare for it.
Whoever intends to do a good deed and does what he can to prepare for it, it
will be recorded for him (as if he did it). Allaah says (interpretation of
the meaning): 

“He who emigrates (from his home) in the Cause of Allaah,
will find on earth many dwelling places and plenty to live by. And whosoever
leaves his home as an emigrant unto Allaah and His Messenger, and death
overtakes him, his reward is then surely, incumbent upon Allaah”

[al-Nisa’ 4:100]

If this man had sold all his wealth in order to do Hajj
because Hajj is an Islamic duty, then Hajj should be performed on his behalf
after his death, using this money that he had prepared, by one of his heirs
or by someone else. According to the hadeeth of Ibn ‘Abbaas (may Allaah be
pleased with him), a woman came to the Prophet (peace and blessings of
Allaah be upon him) and said: “O Messenger of Allaah, my mother vowed to do
Hajj but she did not do Hajj before she died. Can I perform Hajj on her
behalf?” He said: “Yes.” That was during the Farewell Pilgrimage. End
quote. 

Fataawa Ibn ‘Uthaymeen, 21/232 

He was also asked: A man came from his homeland to perform
Hajj, but the plane crashed before reaching (Saudi Arabia). Is he regarded
as a hajji? 

He replied: 

If a person who is travelling to Hajj dies before setting
out, he is not a hajji, but Allaah will reward him for his deeds. If he had
entered ihraam and then died, then he is a hajji, because the Prophet
(peace and blessings of Allaah be upon him) said concerning a man whose
she-camel broke his neck whilst he was standing in ‘Arafah: “Wash him with
water and lotus leaves, and shroud him in his two garments, but do not apply
perfumes to him or cover his head, for he will be raised on the Day of
Resurrection reciting the Talbiyah.” He did not tell them to make up his
Hajj, which indicates that he was a hajji. End quote. 

Fataawa Ibn ‘Uthaymeen, 21/252.