I see four main problems:
1. You are using 3.3V. Datasheet shows values for 3.6V. I would expect that the gain with 3.3V would be similar to 3.6V (but with lower Psat), but you can't be certain. Datasheet numbers are USUALLY very good guidance of what the part will do. BUT you have to follow ALL the criteria.
2. You say Vpd=3.3V. This is one of your primary problems. The datasheet specifies that with a 3.6V supply (or a 5V supply), Vpd should be 3.6V at the IC pins NOT the demo board Vctrl. The datasheet specifies that the current into the Vpd pins at 3.6V is 7 mA. Therefore resistors R1 and R2 must be chosen to give 7 mA. You have not followed this, therefore your gain is not maximum.
3. Your spectrum analyzer OCBW mode is nice feature, but it is going to show the average power. With 27 dBm average power and an OFDM waveform, your peak power will most certainly be much higher and therefore clipped (saturated). You are overdriving the amp. Put a way lower signal in. Add an attenuator at the input if you can't tone down the input power of your source.
4. This one is also about overdriving your source, but with the VNA. If you can't reduce the source signal of the VNA, you have to put an attenuator at the amp input.
Datasheets are your friend, but you have to read through them and follow everything they talk about doing. You don't have the correct Vpd, and you are overdriving the amp. Anytime I measure a power amplifier with a VNA, I will ALWAYS (ALWAYS ALWAYS) put an attenuator on port 2 to protect my VNA from damage, and I will turn down the source power to a small value. If my amp had 20 dB gain, I'd turn it down to -20 dBm. If I had a VNA that couldn't do that, I'd put a 20 dB attenuator on port 1. Calibrate the VNA with PADs on the ports and the resulting through should measure S21=0dB. For things like this I use a simple THRU cal if the VNA supports that. Insert device under test and read the gain. If my S21 reading then didn't match the datasheet number, I'd assume I was doing something wrong. THEN and ONLY THEN would I start to raise the input level to see where the gain started to compress.