I can add it appears also on the site I used to generate that Zalgo text:

https://eeemo.net/

Interestingly, only up and down diacritics cause the square issue, every time I just check the middle diacritic there is no issue.

so looking at the javascript code on the above text generator, one can assume only the unicodes responsible for the square rendering issue are in the zalgo_up and zalgo_down arrays :

			// data set of leet unicode chars
			//---------------------------------------------------

			//those go UP
			var zalgo_up = [
				'\u030d', /*     ̍     */		'\u030e', /*     ̎     */		'\u0304', /*     ̄     */		'\u0305', /*     ̅     */
				'\u033f', /*     ̿     */		'\u0311', /*     ̑     */		'\u0306', /*     ̆     */		'\u0310', /*     ̐     */
				'\u0352', /*     ͒     */		'\u0357', /*     ͗     */		'\u0351', /*     ͑     */		'\u0307', /*     ̇     */
				'\u0308', /*     ̈     */		'\u030a', /*     ̊     */		'\u0342', /*     ͂     */		'\u0343', /*     ̓     */
				'\u0344', /*     ̈́     */		'\u034a', /*     ͊     */		'\u034b', /*     ͋     */		'\u034c', /*     ͌     */
				'\u0303', /*     ̃     */		'\u0302', /*     ̂     */		'\u030c', /*     ̌     */		'\u0350', /*     ͐     */
				'\u0300', /*     ̀     */		'\u0301', /*     ́     */		'\u030b', /*     ̋     */		'\u030f', /*     ̏     */
				'\u0312', /*     ̒     */		'\u0313', /*     ̓     */		'\u0314', /*     ̔     */		'\u033d', /*     ̽     */
				'\u0309', /*     ̉     */		'\u0363', /*     ͣ     */		'\u0364', /*     ͤ     */		'\u0365', /*     ͥ     */
				'\u0366', /*     ͦ     */		'\u0367', /*     ͧ     */		'\u0368', /*     ͨ     */		'\u0369', /*     ͩ     */
				'\u036a', /*     ͪ     */		'\u036b', /*     ͫ     */		'\u036c', /*     ͬ     */		'\u036d', /*     ͭ     */
				'\u036e', /*     ͮ     */		'\u036f', /*     ͯ     */		'\u033e', /*     ̾     */		'\u035b', /*     ͛     */
				'\u0346', /*     ͆     */		'\u031a' /*     ̚     */
			];

			//those go DOWN
			var zalgo_down = [
				'\u0316', /*     ̖     */		'\u0317', /*     ̗     */		'\u0318', /*     ̘     */		'\u0319', /*     ̙     */
				'\u031c', /*     ̜     */		'\u031d', /*     ̝     */		'\u031e', /*     ̞     */		'\u031f', /*     ̟     */
				'\u0320', /*     ̠     */		'\u0324', /*     ̤     */		'\u0325', /*     ̥     */		'\u0326', /*     ̦     */
				'\u0329', /*     ̩     */		'\u032a', /*     ̪     */		'\u032b', /*     ̫     */		'\u032c', /*     ̬     */
				'\u032d', /*     ̭     */		'\u032e', /*     ̮     */		'\u032f', /*     ̯     */		'\u0330', /*     ̰     */
				'\u0331', /*     ̱     */		'\u0332', /*     ̲     */		'\u0333', /*     ̳     */		'\u0339', /*     ̹     */
				'\u033a', /*     ̺     */		'\u033b', /*     ̻     */		'\u033c', /*     ̼     */		'\u0345', /*     ͅ     */
				'\u0347', /*     ͇     */		'\u0348', /*     ͈     */		'\u0349', /*     ͉     */		'\u034d', /*     ͍     */
				'\u034e', /*     ͎     */		'\u0353', /*     ͓     */		'\u0354', /*     ͔     */		'\u0355', /*     ͕     */
				'\u0356', /*     ͖     */		'\u0359', /*     ͙     */		'\u035a', /*     ͚     */		'\u0323' /*     ̣     */
			];
			
			//those always stay in the middle
			var zalgo_mid = [
				'\u0315', /*     ̕     */		'\u031b', /*     ̛     */		'\u0340', /*     ̀     */		'\u0341', /*     ́     */
				'\u0358', /*     ͘     */		'\u0321', /*     ̡     */		'\u0322', /*     ̢     */		'\u0327', /*     ̧     */
				'\u0328', /*     ̨     */		'\u0334', /*     ̴     */		'\u0335', /*     ̵     */		'\u0336', /*     ̶     */
				'\u034f', /*     ͏     */		'\u035c', /*     ͜     */		'\u035d', /*     ͝     */		'\u035e', /*     ͞     */
				'\u035f', /*     ͟     */		'\u0360', /*     ͠     */		'\u0362', /*     ͢     */		'\u0338', /*     ̸     */
				'\u0337', /*     ̷     */		'\u0361', /*     ͡     */		'\u0489' /*     ҉_     */		
			];

I can also add it works perfectly fine on my laptop with same os (debian buster) and same chromium version ( 71.0.3578.80 ) ...!

So I'm a little bit puzzled and lost as on 2 different desktops with same chromium version and OS, squares appear for some specific unicodes diacritics,

I moved ~/.fonts on laptop, updated the cache and it still works, so the difference between the working / not working might be in the system installed fonts, will investigate and report back, if there is a simpler way to pinpoint why there are squares I'm all ears

Thanks for filing the issue...

As per comment #0, able to reproduce the issue on reported chrome version 71.0.3578.80 also on latest chrome 73.0.3652.0 Ubuntu 17.10.  
 
Same behavior is seen on M60(60.0.3112.113) hence considering it as non-regression and marking it as Untriaged. 

Note:Issue not observed on Mac and Windows 10.

Thanks..!

I created a small docker container that tries to display diacritics added to letters.

It's up and running at https://zalgo.bartab.fr

Code is available at https://github.com/euri10/zalgo should you want to run it.

On my desktop the following unicodes below are rendered as squares, I attach the font list my system has, as per fc-cache -r -v | sort, in the desktop-fonts file:
up diacritics: u0350, u0363 to u36f included, u035b
mid diacritics: none
down diacritics: u0354, u0355, u0356, u0359

On my laptop, same OS, same chromium version, all is rendered correctly, fonts on the system are laptop-fonts attached.

Hope it helps,

Deleted: laptop-fonts 6.7 KB

laptop-fonts 6.7 KB View Download

Deleted: desktop-fonts 4.8 KB

desktop-fonts 4.8 KB View Download

Issu observed on Linux (71.0.3578.98), but not on Mac and Windows.

However, dicacritics are rendered as squares not only in DevTools>Elements, but also on the webpage as well (with or without DevTools open) so the root cause seems to be somewhere in Blink.

Reassign to Blink for better triaging.

Thanks for the report and the additional test cases, Benoit. We're tracking this and similar cases in issue 591346.