CD74HCT125 Question

This would not be good. since it would alway draw max current through that output, It would more than likely damage or degrade the part.

Correction: output is open. But both input and output enable are connect to Vcc directly.

Would this damage the gate?

If yes, how. What's the failure mode.

Is this good practice?

best practice is to tie it to Vcc or gnd through a resistor but most don,t since it is mor trouble and cost.  It is Ok to do it this way. It would be bad to leave them floating.