When specifying a natural gas line, what do you need to call out

I am a practicing electrical engineer in the power industry. Recently at a kickoff meeting, another engineer mentioned that there was the need to bring in a natural gas line at 2-5psi and 4,000,000 Btu.

First off, is it acceptable terminology to refer to a natural gas line/connection point as 4,000,000 Btu?

Engineering wise it may make more sense to talk about a flow rate or energy rate, not Btu which is only a unit for energy. However, I know that when people refer to pouring concrete, the going way of refering to the amount is in yards (instead of cubic yards) even though it doesn't make sense unit wise.

This seems to be a little weird but I'm just wondering if this is another dumb rule or way of communicating that has been popularized - as I looked kind of dumb asking about it at a meeting..

Technically speaking, the proper units for gas line capacity are SCF/Hr (standard cubic feet per hour) at some specified pressure (in your case 2-5 psi)
Since this is an industrial (not residential or light commercial) application, the best bet is to consult with your local utility.
The problem with using Btu to measure capacity is that:
A) type of gas needs to be specified (propane, natural gas, etc); the contain different BTUs per unit
B) Change in Temp = change in Vol = change in total BTU value

However, they may have developed some shorthand (as you say) and in speaking of BTU/Hr, the conversion is close enough so that everyone (vendor, engineer, installer, supplier, etc) is on the same page at the end of the day.

Referring to BTU/Hr is a way of cross-hairing the overall heat (i.,e. fuel) requirement. However equipment efficiency will play a HUGE part in the final analysis of your gas line requirement.
4,000,000 Btu (per HOUR I assume) is not a terribly large load.
As an arbitrary example, the swing of +/- 15% in efficiency may mean the difference between a 6 or 8 in. line.