e-sugoroku is the racing game, it's sense 1.

Koj, Daijr/s: have two senses covering 盤双六 and 絵双六.

Maybe this will work. If approved the 盤双六 and 絵双六 entries need tweaking and relinking.

@@ -37,2 +37,4 @@
-<xref type="see">盤双六</xref>
-<gloss>ban-sugoroku (trad. Japanese board game played with dice)</gloss>
+<xref type="see" seq="2847949">盤双六</xref>
+<xref type="see" seq="2764760">絵双六</xref>
+<s_inf>orig. meaning</s_inf>
+<gloss>trad. Japanese board games played with dice, esp. e-sugoroku and ban-sugoroku</gloss>

if sense 1 refers to ban-sugoroku, then sure. but google images will show that the simpler racing game is much more common. Same with the 
romaji "sugoroku". you have to type out "ban-sugoroku" or 盤双六 to get pictures of the other game.

@@ -33 +33 @@
-<gloss>sugoroku (trad. Japanese board game played with dice)</gloss>
+<gloss>race game (board game where the object is to reach the goal first)</gloss>
@@ -37 +37,2 @@
-<gloss>race game (board game where the object is to reach the goal first)</gloss>
+<xref type="see">盤双六</xref>
+<gloss>ban-sugoroku (trad. Japanese board game played with dice)</gloss>

OK, but that's another sense.

@@ -33,0 +34,4 @@
+</sense>
+<sense>
+<pos>&n;</pos>
+<gloss>race game (board game where the object is to reach the goal first)</gloss>

an example of a simple race game being referred to as sugoroku
https://www.daiichigakuin.ed.jp/campus/kyoto/blog/42867/
plenty of more examples in google images if you search for 英語 すごろく etc.

So the "native informer" I was referring too has on several occasions referred to several non-Japanese race games as 双六, so I do think it 
just means "race game". I was considering making it a separate sense and formatted it like that first but it looked weird to me and I didn't 
think keeping "sugoroku" as an English gloss was all that worthwhile considering that the only thing that sets a "sugoroku" apart from a 
"race game" in English is that the former is Japanese.

GG5: sugoroku; a traditional board game in which pieces are advanced by throwing dice; a 
Japanese backgammon.
中辞典: sugoroku; a Japanese variety of Parcheesi
ルミナス: sugoroku [U], Japanese backgammon [U]; (説明的には) a Japanese game played with a「die 
[《英》 dice].
https://en.m.wikipedia.org/wiki/Sugoroku - refers to two different forms of a Japanese 
board game: ban-sugoroku (盤双六, 'board-sugoroku') which is similar to western backgammon, 
and e-sugoroku (絵双六, 'picture-sugoroku') which is similar to western Snakes and Ladders.

Yes, it's a race game but so are many board games using dice. AFAIK 双六 is not the general 
term for race games in Japanese. I think the Romaji is worth keeping. Maybe this is enough.

@@ -33 +33 @@
-<gloss>race game (type of board game played where the object is to first reach the goal)</gloss>
+<gloss>sugoroku (trad. Japanese board game played with dice)</gloss>

native informer
https://en.wikipedia.org/wiki/Race_game

This word's used for non-Japanese race games too. I don't think "sugoroku" in English really means much except "old or old-ish Japanese 
race game"

@@ -33,2 +33 @@
-<gloss>sugoroku</gloss>
-<gloss g_type="expl">traditional Japanese board game played with dice</gloss>
+<gloss>race game (type of board game played where the object is to first reach the goal)</gloss>

寿語録	54
壽語録	88

saw 寿語録 on an old Meiji 28 print
here's another example: https://www.admt.jp/collection/item/?item_id=18

@@ -12,0 +13,8 @@
+</k_ele>
+<k_ele>
+<keb>壽語録</keb>
+<ke_inf>&ateji;</ke_inf>
+</k_ele>
+<k_ele>
+<keb>寿語録</keb>
+<ke_inf>&ateji;</ke_inf>

koj, daij, wiki

@@ -8,0 +8,3 @@
+<keb>双陸</keb>
+</k_ele>
+<k_ele>
@@ -9,0 +12,1 @@
+<ke_inf>&oK;</ke_inf>
@@ -13,0 +17,6 @@
+<r_ele>
+<reb>すぐろく</reb>
+<re_restr>双六</re_restr>
+<re_restr>雙六</re_restr>
+<re_inf>&ok;</re_inf>
+</r_ele>
@@ -16,1 +26,1 @@
-<gloss g_type="expl">traditional Japanese board game</gloss>
+<gloss g_type="expl">traditional Japanese board game played with dice</gloss>

@@ -15,1 +15,0 @@
-<gloss>child's dice game</gloss>
@@ -17,1 +16,1 @@
-<gloss>traditional Japanese board game</gloss>
+<gloss g_type="expl">traditional Japanese board game</gloss>

wp

@@ -6,0 +6,3 @@
+</k_ele>
+<k_ele>
+<keb>雙六</keb>
@@ -12,1 +15,3 @@
-<gloss>a child's dice game</gloss>
+<gloss>child's dice game</gloss>
+<gloss>sugoroku</gloss>
+<gloss>traditional Japanese board game</gloss>