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I had the same issue on Gentoo.
Two things to make sure:
1. run "tv-setup checklibs" from inside the teamviewer folder, this checks if all required libraries are in place. On Gentoo, you have to manually install some 32bit versions.
2. Teamviewer/Wine doesn't run with freetype > 2.8. If you have the current ~ version installed (2.8.1), it won't open the GUI. A downgrade will solve this.
So this goes to the devs here: This is probably a wine issue. Can we expect a TV version which is compatible to a recent freetype lib?