Psalm 136 is a hymn of thanksgiving to God, and each verse ends with the refrain "for his loving kindness endures forever." This refrain, in Hebrew, is "ki l'olam chasdo." It emphasizes the everlasting nature of God's chesed, which is a complex concept best translated as loving-kindness, steadfast love, mercy, or grace. It's more than just love; it's a loyal, covenant-based, and unwavering commitment to his people.

Verse 19 specifically mentions Sihon, king of the Amorites, immediately after mentioning Egypt (verse 15). This is a key point. God judged and defeated Sihon, just as he judged and defeated Pharaoh. Therefore, the meaning of the verse is not that God showed loving-kindness to Sihon. It means:

God demonstrated his loving-kindness to Israel by defeating Sihon. The destruction of their enemies was an act of chesed towards the Israelites. By removing obstacles, God cleared the path for his people to enter the Promised Land and fulfill His promises to them.
God's actions, even those involving judgment, demonstrate his loving-kindness toward his chosen people. The defeat of Sihon wasn't random violence. It was a necessary step in God's plan to protect and bless Israel, fulfilling His covenant with them. The conquest of Sihon's territory was a demonstration of God's power and faithfulness.
The refrain "for his loving kindness endures forever" emphasizes that God's commitment to his people is unwavering, even when he must act in ways that seem harsh to outsiders. Even acts of judgment are ultimately for the long-term benefit and protection of those who are in covenant with Him.

In essence, Psalm 136:19 reminds us that God's loving-kindness is not a sentimental feeling but a powerful, active force that works for the good of his people, even through judgments and battles. The destruction of Sihon, though seemingly an act of violence, was an act of love and faithfulness to Israel.