Unless one goes through the 'installation process' anew each time one runs the software (this is of course all taking them at their word; I haven't actually analyzed the Tribler source myself), one can then be continuously tracked even when one's IP changes (not only during instances of travelling or being 'mobile', but of course in cases of users having dynamic IPs as well). The fact that one can thus be tracked across multiple IPs is precisely what makes this a cause for concern.
Add to that the statement that the entire Tribler network is 'constantly monitored' (cf. some organizations doubtlessly monitoring some torrent trackers, but it being improbable that every single torrent tracker is monitored), and one once again has a gross escalation of privacy erosion that surpasses the extent of mere IP-based tracking.
"Our technology increases your tracability. Every Tribler software installation has a unique identifier based on Elliptic Curve Cryptography."
"We are constantly monitoring the Tribler P2P network using spider software. This will allow us to detect inefficiencies in our P2P software. However, it will also show us the occurence of illegal activities."
Add to that the statement that the entire Tribler network is 'constantly monitored' (cf. some organizations doubtlessly monitoring some torrent trackers, but it being improbable that every single torrent tracker is monitored), and one once again has a gross escalation of privacy erosion that surpasses the extent of mere IP-based tracking.