Yes, that's typical complete idiot tech support talk. Clearly, as usual, they haven't the first fracking clue what they are talking about and this is EXACTLY why we try to steer people away from prebuilt systems, but we won't go into that. You already have it, so no point in arguing the merits of building your own system at this point.
Of course HDMI supports up to 120hz. In fact, HDMI 1.3 and above will support 144hz, IF the display supports 144hz on the HDMI version that your graphics card (Whatever that might be for any given system) has. So if your graphics card is HDMI 1.3 AND your display supports 144hz on HDMI 1.3, then it will work. If your monitor only supports 144hz over HDMI on HDMI 2.0, then you'd need a 2.0 HDMI capable card.
Freesync and Gsync are supported over HDMI as well, if you have a version that supports it. So, again, idiots.
Andy they do not manufacture them. That alone should be enough to convince ANY sane person that EVERYTHING they say is 100% high grade bullsh#$t. Even companies like Corsair, Antec, Rosewill, NZXT, Fractal design, EVGA and most others, DO NOT manufacture their own power supplies. They are made by companies like Seasonic, Super Flower, CWT, FSP, Great wall, Chicony, HEC, Andyson and Delta. All of whom ARE power supply manufacturers. IF Digital storm has their own power supplies, they are made by somebody else, same as with Antec, Corsair, EVGA, etc., except that many of those companies have both good and really crappy units.
I would suspect that in order to optimize their profit margins, Digital storm likely contracts with one of these companies for VERY bottom of the barrel budget platforms to slap their own labels on. Even so, by law, they MUST comply with providing the unit specifications on a label directly ON the unit, so there will be one there somewhere although you may have to unscrew it from the back of the case, slide it out and to the side and turn the unit in order to get a peek at the label IF this is a case that has a PSU shroud on the motherboard chamber side of the case to where you can't actually see the power supply without taking off the right hand side panel.
I would very much suspect that your poor performance COULD be due to a crappy power supply since you upgraded the graphics card to what is in all probability a much more capable, and power consuming model.