Allah mentioned His sovereignty of the Day of Resurrection, but this does not negate His sovereignty over all other things. For Allah mentioned that He is the Lord of existence, including this earthly life and the Hereafter. Allah only mentioned the Day of Recompense here because on that Day, no one except Him will be able to claim ownership of anything whatsoever. On that Day, no one will be allowed to speak without His permission. Similarly, Allah said,
يَوْمَ يَقُومُ الرُّوحُ وَالْمَلَـئِكَةُ صَفّاً لاَّ يَتَكَلَّمُونَ إِلاَّ مَنْ أَذِنَ لَهُ الرَّحْمَـنُ وَقَالَ صَوَاباً
(The Day that Ar-Ruh (Jibril (Gabriel) or another angel) and the angels will stand forth in rows, they will not speak except him whom the Most Gracious (Allah) allows, and he will speak what is right.) (78:38),
وَخَشَعَتِ الأَصْوَاتُ لِلرَّحْمَـنِ فَلاَ تَسْمَعُ إِلاَّ هَمْساً
(And all voices will be humbled for the Most Gracious (Allah), and nothing shall you hear but the low voice of their footsteps.)(20:108), and,
يَوْمَ يَأْتِ لاَ تَكَلَّمُ نَفْسٌ إِلاَّ بِإِذْنِهِ فَمِنْهُمْ شَقِىٌّ وَسَعِيدٌ
(On the Day when it comes, no person shall speak except by His (Allah's) leave. Some among them will be wretched and (others) blessed) (11:105).
Ad-Dahhak said that Ibn `Abbas commented, "Allah says, `On that Day, no one owns anything that they used to own in the world."'
Ibn `Abbas said, "Yawm Ad-Din is the Day of Recompense for the creatures, meaning the Day of Judgment. On that Day, Allah will reckon the creation for their deeds, evil for evil, good for good, except for those whom He pardons." In addition, several other Companions, Tabi`in and scholars of the Salaf, said similarly, for this meaning is apparent and clear from the Ayah.
Allah is the True Owner (Malik) (of everything and everyone). Allah said,
هُوَ اللَّهُ الَّذِى لاَ إِلَـهَ إِلاَّ هُوَ الْمَلِكُ الْقُدُّوسُ السَّلَـمُ
(He is Allah, beside Whom La ilaha illa Huwa, the King, the Holy, the One free from all defects) (59:23).
Also, the Two Sahihs recorded Abu Hurayrah saying that the Prophet ﷺ said,
«أَخْنَعُ اسْمٍ عِنْدَ اللهِ رَجُلٌ تَسَمَّى بِمَلِكِ الْأَمْلَاكِ وَلَا مَالِكَ إِلَّا اللهُ»
(The most despicable name to Allah is a person who calls himself the king of kings, while there are no owners except Allah.)
Also the Two Sahihs recorded that the Messenger of Allah ﷺ said,
«يَقْبِضُ اللهُ الْأَرْضَ وَيَطْوِي السَّمَاءَ بِيَمِينِهِ ثُمَّ يَقُولُ: أَنَا الْمَلِكُ، أَيْنَ مُلُوكُ الْأَرْضِ؟ أَيْنَ الْجَبَّارُونَ؟ أَيْنَ الْمُتَكَبِّرُونَ؟»
((On the Day of Judgement) Allah will grasp the earth and fold up the heavens with His Right Hand and proclaim, 'I Am the King! Where are the kings of the earth Where are the tyrants Where are the arrogant')
Also, in the the Glorious Qur'an;
لِّمَنِ الْمُلْكُ الْيَوْمَ لِلَّهِ الْوَحِدِ الْقَهَّارِ
(Whose is the kingdom this Day Allah's, the One, the Irresistible.)(40:16).
As for calling someone other than Allah a king in this life, then it is done as a figure of speech. For instance, Allah said,
إِنَّ اللَّهَ قَدْ بَعَثَ لَكُمْ طَالُوتَ مَلِكًا
(Indeed Allah appointed Talut (Saul) as a king over you.) (2:247),
وَكَانَ وَرَآءَهُم مَّلِكٌ
(As there was a king behind them)(18:79), and,
إِذْ جَعَلَ فِيكُمْ أَنْبِيَآءَ وَجَعَلَكُمْ مُّلُوكاً
When He made Prophets among you, and made you kings )5:20(.
Also, the Two Sahihs recorded,
«مِثْلُ الْمُلُوكِ عَلَى الْأَسِرَّةِ»
(Just like kings reclining on their thrones)
Ad-Din means the reckoning, the reward or punishment. Similarly, Allah said,
يَوْمَئِذٍ يُوَفِّيهِمُ اللَّهُ دِينَهُمُ الْحَقَّ
(On that Day Allah will pay them the (Dinahum) recompense (of their deeds) in full) (24:25), and,
أَءِنَّا لَمَدِينُونَ
(Shall we indeed (be raised up) to receive reward or punishment (according to our deeds)) (37:53). A Hadith stated,
«الْكَيِّسُ مَنْ دَانَ نَفْسَهُ وَعَمِلَ لِمَا بَعْدَ الْمَوتِ»
(The wise person is he who reckons himself and works for (his life) after death.) meaning, he holds himself accountable. Also, `Umar said, "Hold yourself accountable before you are held accountable, weigh yourselves before you are weighed, and be prepared for the biggest gathering before He Whose knowledge encompasses your deeds,
يَوْمَئِذٍ تُعْرَضُونَ لاَ تَخْفَى مِنكُمْ خَافِيَةٌ
(That Day shall you be brought to Judgement, not a secret of yours will be hidden) (69:18)."