Does not writing a checkpoint record damage anything?
Does the failed checkpoint write (by its self) cause any damage that I might need to address?


There would be no damage as such, what checkpoint does is it writes dirty pages from buffer pool to the disk reducing the amount of recovery time and amount of work SQL Server has to do after restart or crash recovery. In extreme case if database goes under crash recovery the amount of time taken to recover database would increase.

In your case it is good you found out that it was actually the index rebuild which produced some good amount of logs and eventually failed because of low disk space on log drive. This would just rollback the operation and would bring fragmentation as it was before the rebuild