Card game, and being able to turn off lights at any time are very good hints!
Based on this, I believe it is either gyaoppi chicken, or their shortened clones, tamakachi chickens: tamakachi chicken program is very much like gyaoppi, with one minus: the weather event (sun, rain, equipping hats/umbrellas) are unique to gyaoppi based programs. Tamakachis do not have weather function, but often there is a 'mood' function which shows the hapiness meter of the pet as a seperate function. There are many variants based on these.
Chuppi shared above is the original gyaoppi chicken. Has weather event.
There is smart chick, a tamakachi chicken. Shown here in this video
Chick duck is a very similiar, too. There is also birdwatching gyaoppi chicken, but it is gyaoppi 1 programming: you can turn off the lights but the pet does not go to sleep! It goes to sleep in its own schedule, based on actual clock. Gaaa hippie is also very similiar.
Oh, here in this page there is pet shaped like you described, at the bottom of the page, with all bird/chicken vpets:
http://www.tamenagerie.com/odd18.html
kookoo chicken? unfourtunately googling it does not help, but you can find all these other programmings relatively easily. They are pretty much same with some minor differences.
If you are into gyaoppi based programs, super gyaoppi 9in1 is very easy to find on ebay, and it has the chicken in it plus 8 other animals. It is overall the best and easiest to purchase today of all these gyaoppi based programmings. Here I played with the duck:
https://www.tamatalk.com/threads/super-gyaoppi-duck-log-comments-ok.201363/