If he prayed without facing towards the qiblah because he forgot, does he have to repeat it?

Firstly: 

In order for prayer to be valid, it is stipulated that one
should face towards the qiblah. If one does not pray facing towards the
qiblah when one is able to do so, then the prayer is invalid, because Allah,
may He be exalted, says (interpretation of the meaning):

“so turn your face in the direction of Al-Masjid- al-Haram
(at Makkah). And wheresoever you people are, turn your faces (in prayer) in
that direction”

[al-Baqarah 2:144].

And the Prophet (blessings and peace of Allah be upon him)
said, in the hadeeth about the one who prayed badly: “Then turn towards the
qiblah and say Allahu akbar.”

Narrated by al-Bukhaari, 6667. 

Ibn Qudaamah (may Allah have mercy on him) said: Six things
are stipulated with regard to the prayer – among which he mentioned facing
towards the qiblah. If any of these conditions are not met, with no excuse,
then his prayer is not valid.

End quote from al-Mughni, 1/369 

Secondly: 

The scholars (may Allah have mercy on them) stated that if a
person prays without facing towards the qiblah because he forgot, then he
should repeat his prayer, because he has omitted one of the conditions of
prayer. 

Ibn Hazm (may Allah have mercy on him) said: If a person
prays without facing towards the qiblah when he was able to work out its
direction – whether he does that deliberately or because he forgot, then his
prayer is invalid and he should repeat it so long as there is still time to
do so, if he did that deliberately. And he should repeat it at any time if
he forgot.

End quote from al-Muhalla, 2/259 

The scholars of the Standing Committee for Issuing Fatwas
were asked: What is the ruling on a person who goes to another city and
prays without facing the qiblah by mistake, even though he knows the
direction of the qiblah, then he remembers that after the time for the
prayer that he offered has ended? 

They replied: If a person offers a prayer without facing
towards the qiblah out of negligence, in that he did not ask and he did not
look at the signs that point to the direction of the qiblah, then he should
repeat the prayer, because facing towards the qiblah is one of the
conditions of prayer being valid when one is able to do it. So he has to
repeat the prayer. The same also applies to one who prays without facing
towards the qiblah by mistake. He has to repeat the prayer because he failed
to fulfil one of its conditions. And Allah is the source of strength. 

End quote from Fataawa al-Lajnah ad-Daa’imah, vol. 2,
5/294 

Based on that, you have to repeat this prayer now that you
offered without facing the direction of the qiblah. 

And Allah knows best.