Is this a thing?

Here's my most recent game...

White's early play seemed really weird to me. Setting up a zig zag of all his pawns which, whilst clogging up the middle of the board, was quite easy to unpick. Is this a thing?

Also, I hasten to point out that the reason I lost is because my internet router turns off at midnight. I ran to turn it back on but I didn't reconnect in time. Otherwise I'd have mated him in a few more moves. Nevermind.

Good development at the start, compared to your opponent's suicidal pawn pushing.

11...exf3 e.p. should win very quickly, opening the e-file and threatening ...Qg3+. If white had played 12. hxg5 in the game, he'd have lasted a lot longer.

14. Kd2?? (Kf1 better) and 19. Rh1?? handed you the game.

You missed the incredibly pretty 22...Bd1+ 23. Kc1 Nb3#.

25...Rxd2+ by the power of double check is devastating. If 26. Kc1 Nb3#; 26. Ke1 Re2+ and you have a windmill going.

Unfortunate disconnection. You seem a fair bit stronger than your opponent, so try playing higher-rated people.

Thank you for your tips. I've played through some of the moves you suggested and I found it really helpful.

A direct answer: no, there are no standard pawn only openings.  It can be done against a weak opponent with some success, or even trick a moderate opponent with careful support from a piece or 2, but as for it being a "thing"?  Well, its a "thing" --- its a gimmick, possibly frustrating in super fast chess (game in less than 5 min type stuff) or used against weak players etc. 

There are a couple of pawn intense openings (also, for the most part, gimmicks).  A common example is the hedghog.  It is uncommon to do 3+ pawn moves without a piece, and opening theory generally frowns on doing that.