I suggest (your) choosing a game instead of a movie=I suggest you choose a game.
Suggest is followed by a gerund or by an independent clause. It is like recommend and advise.
What that list of verbs means to avoid is this:
I suggest to go to a movie. instead of: I suggest we go or I suggest going to a movie. or things like: I enjoy to go to a movie. Instead of: I enjoy going to the movies.
The other ones in the list can only take a gerund: enjoy playing tennis; mind opening the window;fancy having a drink;finish doing the work, etc. ( I don't particularly fancy writing examples for every single one.)
suggest is part of a category of verbs that can take a gerund or an independent clause (I hope I got them all), unlike the others on that list.
- I suggest we leave now. I suggest leaving now.
- I advise leaving now. I advise we leave now.
- He recommends finishing early. He recommends we finish early.
- They advised publishing the book. They advised we publish the book.
- We denied damaging the car. We denied we damaged the car.
These verbs that can go both ways as shown above are: suggest, recommend, advise, deny.
careful with imagine: I imagine we left at six o'clock. [think] I imagined we left at six o'clock. [it was something in my imagination]
Sometimes verbs are in two categories and sometimes only in one in terms of how they can be used.