The use of the world, "world" there is talking about the world system - the world order. It's referring to the "badness" of the world, not the "bigness" of the world. In other words, it does not say, God loved every single person, without exception, in this manner, that He gave. . . It says, God loved this evil place in such a manner, He gave. . .
Does God Love Everyone the Same?
You may want to rephrase that statement. God doesnt love the world system, its antithetical to Him. You choose God or the world. Kosmos is just a catch phrase for "all", "everybody"...
To find out what kind of love God has for us we must study all the analogies/parables used in the Bible.
However, we know , parables do not walk on all fours: the analogy fails after a certain point, there is no full one to one correspondence. For example in the parable of the lost coin, God rejoices when the coin which was lost is found. But we do not share the other attributes of the coin, except for the lost experience.
We know that God loves us.
Let's consider what kind of love God really has for us.
Is it the love of an artist/builder for his painting/building?
The Bible does say we are God’s temple, where His Holy Spirit dwells. But sometimes we allow ungodly things or persons into our lives, and the analogy fails, because it is a caretaker who allows trespassers to unlawfully enter a building.
Is it the love of a master/leader for a servant/team member?
Sure the Bible uses the example of a master/servant relationship, but Jesus teaches that it a temporary phase, because He tells His disciples that He no longer calls them servants, but friends
However, the love that is manifested by laying down your life is more closer to the love that a parent or brother or spouse or other family member manifests for another member than the love of a friend for a friend, so are we family?
Sufficiently confused?
Since we see all the analogies of house, servant, friend, family laid out, and are confused by what the love is for, the best option is to choose the analogy which has the most boxes checked.
We are family in the sense He is our Father, but He cares for us in the sense that we have the potential to grow into His likeness. In the sense that we are potentially capable of manifesting His image, we are seeds. He has provided everything in every sentient human the ability to do this. Those who do mature as desired when nurtured, guided, pruned, grafted, continue into life. He has a lot invested in every seed, possibly sacrificially, and the result isn't anything to be sneezed at, and again, possibly, priceless, ie not achievable any other way.
Those who are yet to mature through age, or can not mature because of physical inability, Scripture tells us that their angels always have their faces turned towards God. They are in their natural state, having no responsibility for contributing any input in terms of manifesting the full image of God. They are still seed, but God's seed still.
Those who consciously refuse to respond to the nudging of God's revelations and instructions through nature, conscience, or law finally face the fate of the unfruitful plant. Meant only to be cut down and consigned to the bonfire.
But see how much leeway, mercy and care is shown before that happens:
Let's give extra nurturing and wait for a year says the Master to the gardener, before deciding that the plant is wasting the resources used for its growth.
It is not that God’s love is unconditional which makes it marvelous and wonderful. It is the compassion and mercy that that love is filled with and rides on which is:
Exodus 34:6
Then the LORD passed by in front of him and proclaimed, "The LORD, the LORD God, compassionate and gracious, slow to anger, and abounding in lovingkindness and truth;
Psalm 86:5
For You, Lord, are good, and ready to forgive, And abundant in lovingkindness to all who call upon You.
Psalm 103:8
The LORD is compassionate and gracious, Slow to anger and abounding in lovingkindness.
Psalm 111:4
He has made His wonders to be remembered; The LORD is gracious and compassionate.
Psalm 116:5
Gracious is the LORD, and righteous; Yes, our God is compassionate.
Psalm 145:8
The LORD is gracious and merciful; Slow to anger and great in lovingkindness.
Ecclesiastes 8:11
Because the sentence against an evil deed is not executed quickly, therefore the hearts of the sons of men among them are given fully to do evil.
Isaiah 63:7
I shall make mention of the lovingkindnesses of the LORD, the praises of the LORD, According to all that the LORD has granted us, And the great goodness toward the house of Israel, Which He has granted them according to His compassion And according to the abundance of His lovingkindnesses.
Jeremiah 3:12
"Go and proclaim these words toward the north and say, 'Return, faithless Israel,' declares the LORD; 'I will not look upon you in anger. For I am gracious,' declares the LORD; 'I will not be angry forever.
Jonah 4:2
He prayed to the LORD and said, "Please LORD, was not this what I said while I was still in my own country? Therefore in order to forestall this I fled to Tarshish, for I knew that You are a gracious and compassionate God, slow to anger and abundant in lovingkindness, and one who relents concerning calamity.