The image is autogenerated with the below description using the command dot from the Graphviz package.

Feel free to patch this code, or to talk about it in his talk page.

// dot -oengine.svg -Tsvg engine.dot
digraph {
	ratio=auto;
	sep="+4,5";

	// =============================
	// Engines
	// =============================
	node [shape=polygon, sides=6, style=filled]

	// id Tech engines
	node [peripheries=4, size=6]
    fontsize=20
	// id Tech engines under GPL
	node [fillcolor=lightgreen]
    //Quake
	QuakeE [label="Quake engine"]
	GLQuake
	WinQuake
	QuakeWorld

	Quake2E [label="Quake II engine"]
	idTech3 [label="id Tech 3\nQuake III Arena engine"]
	idTech4 [label="id Tech 4\nDoom 3 engine"]

	// id Tech under commercial license
	node [fillcolor=lightgrey]
	idTech5 [label="id Tech 5"]
    idTech6 [label="id Tech 6"]
    idTech7 [label="id Tech 7"]

	// Other engines
	//
	node [peripheries=1]

	// Other commercial engines
	node [fillcolor=lightgrey]
	GoldSrc
	SourceEngine [label="Source Engine"]
    Source2 [label="Source 2"]

	// Other libre/open engines
	node [fillcolor=lightgreen]
	DarkPlaces

	// =============================
	// Games
	// =============================
	node [shape=ellipse, color=transparent]

	// Commercial Games
	node [fillcolor=lightgrey]
	// id and Bethesda
	Quake
	HexenII [label="Hexen II"]

	QuakeII [label="Quake II"]

	QuakeIIIArena [label="Quake III Arena"]
	QuakeLive [label="Quake Live"]

	Doom3 [label="Doom 3"]
	Quake4 [label="Quake 4"]

	Rage
	WolfensteinTNO [label="Wolfenstein: The New Order"]
	WolfensteinTBO [label="Wolfenstein: The Old Blood"]

	Doom2016 [label="Doom (2016 video game)"]
	Dishonored2 [label="Dishonored 2"]
	Wolfenstein2 [label="Wolfenstein II: The New Colossus"]
	WolfensteinYB [label="Wolfenstein: Youngblood"]

	DoomEternal [label="Doom Eternal"]

	// GoldSrc & Source
	HalfLife [label="Half-Life"]
	TFC [label="Team Fortress Classic"]
	CS [label="Counter-Strike"]
	DoD [label="Day of Defeat"]

	Halflife2  [label="Half-Life ²"]
	DoDS [label="Day of Defeat: Source"]
	gmod [label="Garry's Mod"]
	l4d [label="Left 4 Dead"]
	portal [label="Portal"]
	HLA [label="Half-Life: Alyx"]

	Titanfall
	titanfall2 [label="Titanfall 2"]
	
	COD [label="Call of Duty"]
	
	// Freeware games
	node [fillcolor=lightblue]
	TF2 [label="Team Fortress 2"]
	csgo [label="Counter-Strike: Global Offensive"]
	dota2 [label="Dota 2"]
	apex [label="Apex Legends"]

	// Libre/open games
	node [fillcolor=lightgreen]

	// =============================
	// Trees
	// =============================

	QuakeE -> Quake2E -> idTech3 -> idTech4 -> idTech5 -> idTech6 -> idTech7

    QuakeE -> {WinQuake,GLQuake,QuakeWorld,DarkPlaces}
	QuakeE -> {Quake,HexenII}
    {QuakeWorld,GLQuake,WinQuake} -> Quake
	Quake2E -> QuakeII
	idTech3 -> {QuakeIIIArena, COD, QuakeLive}
	idTech4 -> {Doom3, Quake4}
	idTech5 -> {Rage,WolfensteinTNO,WolfensteinTBO}
	idTech6 -> {Doom2016,Dishonored2,Wolfenstein2,WolfensteinYB}
	idTech7 -> DoomEternal

    GoldSrc -> SourceEngine -> Source2
    {QuakeWorld,Quake2E,QuakeE} -> GoldSrc
	GoldSrc -> {HalfLife,TFC}
	HalfLife -> {DoD,CS}

	SourceEngine -> {Halflife2,DoDS,TF2,l4d,portal,csgo,dota2,Titanfall,gmod}

	Source2 -> {dota2,HLA}

	Titanfall -> titanfall2 -> apex
}

I, the copyright holder of this work, release this work into the public domain. This applies worldwide. In some countries this may not be legally possible; if so: I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.