Your installation should be OK. If it's not you would see big yellow flames from the incomplete combustion of the NG.

Is that a big gap underneath?

If the backside isn't stone then a small vent could be drilled in.

Yes big gap underneath. All sides are stone. Does it still need to be vented? I’m thinking below the grill should be closed in with stone but then the installers told me it needs vents on both sides? And we really don’t have room for a vent besides the hole directly under the grill

If you using Natural Gas and there is a leak, the gas will rise to the top and most likely it will escape through the vents in the grill. If you will have Propane gas propane gas is heavy so instead of rising, it will sink to the bottom of the enclosed structure and it will collect there, so if the enclosed space doesn't have ventilation it can cause an explosion when someone lights something, etc. So it's a good idea to install a vent register on the other side as a safety precaution and have air circulation under there so if it does happen the gas can escape.

That being said, if everything maintained and there are no corroded gas line connections which can cause a leak, the chances are slim to none that will ever happen, but then again, this is gas and it can explode and if there is an issue... it only takes 1 time and its "kaboom".

Good luck