To clarify, there are no four-character words starting with 題, but there are four-character words that start with 問題. This appears to be the game in question.
I’m surprised I’ve never encountered this. I wonder if it is a recent regression.
When doing look-aheads, renshuu only checks single-character overlaps. Those are actually the only "real" plays that can be made in shiritori - the double characters are added as a bonus.
I think the error message could be reworded to be a little more precise. Something like “Sorry, but there are no words starting with 題 that can be played off this.”