“The only way to win is to refuse to play”
Is this team-building crap being done on company time? If so, go to TBTB and say that you have real work to do. Could they give you deadline extensions in writing for your current projects? If it’s not, tell them you’ll formally file a complaint about being made to do work off the clock.
Or explain that you find it intrusive and that it makes you uncomfortable. Being able to compose poetry about a fellow teammate’s personal qualities is inappropriate in a workplace. If you’ve been moved into a position of authority where you are to judge her professional skills, you’ll need uptraining and an increase in salary commensurate with your new position, plus at least 3 months of observation of her in a supervisory capacity before you can give a good performance evaluation.
Then say: I hope I’m not misunderstanding. You’re not asking me to comment on her personal likes, dislikes, issues and situation. Because that’s wildly inappropriate workplace conduct. And you’ll certainly be going to HR or calling the company Ombudsman if someone has the audacity to presume to give you a recipe for how to live your life.
…or, if you don’t want the nuclear option, 
Offer this to your PTB and ask them if it’s appropriate:
A cup of Christ upon the Cross
3 pints of blood he spilled
2 real sharp spears stuck in his side
A long night on that hill
He came from death to give us all
This swell life’s recipe
And if you ignore his sacrifice
You’ll go to hell, not me.
(Yeah, the scansion’s off–it’s 7:45 here. Whaddaya want? Robert Frost?)
This is best if your pregnant lady is Jewish/Hindu/Muslim/Atheist.
Make them explain why that personal bit of gurge is ok, but other comments on your coworker’s personal qualities and unasked for advice on her personal life are acceptable.
Warning: Do these at your own risk. You’ll probably get out of having to do this crap, but you’ll be a known troublemaker.